These larger hexagons become the individual units, rather than the small hexagons traced out by the carbon atoms.
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The rods adjust their orientation around the hexagons, and the interaction between the rods and hexagons governs the rules of this strange realm.
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Beginning with a field of white hexagons, she created 'florets' by choosing one tile to be left unpainted while incrementally coloring the hexagons around it into an asymmetrical 'flower.
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His Trochumetrics series features intricate mosaics of tessellating stars and hexagons.
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To honor Rita, Downey conscripted volunteers to finish the 100 hexagons.
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After much searching, we find the perfect-sized marble mosaic hexagons.
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Scrawled upon a handwritten map is a curious symbol of interlocking hexagons.
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That can drill down into foods, animals, or even patterns like hexagons.
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And then—boom—the molecules stack into little hexagons, and you've got ice.
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A man obsessed with hexagons tried to remake the visual world around him.
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Our examples above use equilateral triangles (regular triangles), squares (regular quadrilaterals) and regular hexagons.
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Instead, I spent time floating through a prehistoric sea and faux-hacking through hexagons.
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From any of the hexagons one can see, interminably, the upper and lower floors.
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Each HEX condom integrates 350 small hexagons through its latex surface, resulting in effective performance.
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Once this happens, the bonds in the adjacent hexagons also break, unzipping the entire tube.
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Using a sliding table saw, the sheets are cut into squares, hexagons and other shapes.
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Regular water ice is called ice Ih, ice one-h, and its molecules line up into hexagons.
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Think about tiling a bathroom floor, using just tiles in the shape of triangles, squares or hexagons.
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This converted two of the hexagons into a pentagon and heptagon, creating a malformation in the tube.
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The designers decided to preserve a pattern of gradually inflating hexagons, with five landings on every floor.
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The arc of hexagons above her left eyebrow is speciogynine, thought to be a smooth muscle relaxer.
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For his part, Liebreich showed a chart depicting the mix of global energy supply, as represented by hexagons.
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It's repeating hexagons of these ball-like carbon atoms that extend on in atomic scales for great distances.
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In that trip, Shannon saw a floor thick with networks, hexagons, traffic and lights, and many other things.
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Any company can make a connected thermostat, but only Johnson Controls made a connected thermostat with hexagons on it.
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To make things even worse, bright hexagons flash in front of you every time you're going back in time.
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As usual, the new World Cup brings a new FIFA ball: This year's is white with gray pixilated hexagons.
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"I made the hexagons for the first time there, a fifty-foot wall, twelve feet up," he told me.
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At various points in the painting she will make a diagonal line, seemingly guided by the dots of the hexagons.
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The hexagons of honeycomb, as drawn by Arsenault, seem so perfect as to be fanciful precisely when they are fact.
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In "knots + surfaces" (2001), honeybees perform their dance across multicolored hexagons, which are projected onto the gallery walls and floor.
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You start playing with them—squares, rectangles, triangles and hexagons—moving them around, flipping them over, seeing how they fit together.
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Logistics, of course, prevented the Norian House from featuring just hexagons, although Brewster tried to avoid the right angle whenever possible.
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On the black grounds she forms a pattern in which all the dots are integral to the corners of two hexagons.
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And the way the hexagons, each the size of a manhole cover, have been bunched into clusters feels natural and sensible.
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Those hexagons were conceived to be good neighbors — letting sunlight more easily reach the adjacent mid-rise buildings on the estate.
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The systems are pretty interesting because they form all sorts of beautiful patterns—spiral waves, hexagons, target patterns, stripes, and pulses.
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ASL is a game of drab counters on green and brown hexagons, and the SS units are in bold black-and-white.
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First introduced in 1931 at a station in Fukui, the stamps soon proliferated across the country, shaped like circles, squares, pentagons, and hexagons.
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No two visits will be the same, as the arm, like an ever-industrious spider, weaves new hexagons for the carbon fiber forest.
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Instead, the board is created anew each and every game as players take turns placing hexagons featuring different bugs adjacent to each other.
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One of the hidden gems was a massive quilting project combining 113 embroidered hexagons, half with state motifs and the other half with stars.
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The charred sugar beads do the same, falling into a pattern somewhere between interlocking hexagons and squares, depending on how symmetric the beads are.
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Satellite images of newly explored sites within the Upper Tapajós Basin revealed 104 examples of earthworks, in the form of circles, hexagons, and squares.
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For the research center, computers programmed for energy conservation did the same, distorting the hexagons, a rational process producing woozy but climate-efficient forms.
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Ms. Farmanfarmaian also made intricate drawings whose interlocking circles and hexagons translated the tropes of Islamic decorative arts into a realm of pure form.
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The holes are all hexagons, so that again pulls from the hive, but it also pulls from trypophobia and bees, the anonymity of the hive mind.
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"It's gonna be a thing" Once the designs are all stitched and the hexagons are returned to Downey, they will be assembled into the completed quilt.
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According to the ancient Roman scholar and writer Marcus Terentius Varro, a structure made of hexagons is more compact than one made from squares or equilateral triangles.
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A 150-foot-tall cluster of futuristic stair-filled hexagons is coming to New York City's Hudson Yards, courtesy of British starchitect Thomas Heatherwick and Heatherwick Studio.
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She mailed out 100 packages, and has recruited more than 30 Chicago-based quilters to help put the project together once her volunteers turn in their hexagons.
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The signs display a set of icons in the form of stackable hexagons, derived in part from a set of design rules developed by Google in 2014.
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Somehow, lots of individual protein pieces combine to form a capsule, like the hexagons and pentagons of a soccer ball or the triangles on a twenty sided die.
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Images were beamed down minutes or hours after they were taken, he said, as opposed to waiting days or weeks for them to be dropped, like the Hexagons.
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Imagine opening up the connected York Thermostat 280 app with patent-pending hexagon interface, and being able to tap hexagons on the run to remotely control your home.
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Currently there are 1003 people stitching individual hexagons representing the states, and Downey said she has more than 30 Chicago-area quilters ready to put it all together.
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The intense labor of some of those made in convalescence — one from 1890 involves 25,000 blocks, hexagons, and diamonds — represents the incredible amount of time these men spent recovering.
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It's been transformed into a skeletal formula, a series of hexagons with single and double bond lines between them, commonly used to represent carbon and hydrogen atoms in organic chemistry.
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The two layers normally can't communicate, and waves traveling between the two would mean that one hexagon wouldn't quite align with the other—and yet, the observations show aligned hexagons.
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And it was, in part, the lattice structure of the geodesic dome, a convex polyhedron assembled from hexagons and pentagons, themselves divided into triangles, that would inspire Caspar and Klug's theory.
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For instance, you "might do one wall of a walk-in shower in a particular shape, like hexagons," said Jamie Chappell, the creative director of the San Francisco company Fireclay Tile.
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Unlike hexagons, however, regular pentagons cannot be built from equilateral triangles, nor can they tessellate a plane: When slid next to each other to tile a surface, gaps and overlaps inevitably arise.
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The trick they came up with is to reshape keys from squares to honeycomb-style hexagons which allows individual keys to be a bit larger, thereby, they claim, reducing the likelihood of typos.
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I placed my bench fairly close up, slightly off to one side, and I could see the girl's lovely dark eyes under her bangs, the little hexagons of shadow cast by leaves swaying in the breeze.
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But for cryogenic testing, NASA engineers unfurled the mirrors, as well as the telescope's secondary mirror located on the craft's tripod; the secondary mirror will reflect the light gathered from the gold hexagons onto JWST's main instruments.
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A few years later, she replaced the venetian blinds with black shutters, swapped the nickel pulls and plumbing fixtures for brass ones, and repainted the floor with a pattern of interlocking hexagons in two shades of blue.
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They are often doubled and roughly carpentered into various geometric configurations: triangles, the Star of David, divided hexagons opening to sections of shag bath mat, evoking an uncomfortable domestic intimacy while functioning as a kind of under-support.
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There's also a large symbol on the map, two interlocking hexagons that look almost identical to the symbol found in the secret drone host facility that Bernard (Jeffrey Wright) and Charlotte Hale (Tessa Thompson) visited earlier this season.
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His Nobel Prize-winning discovery, which he shared with Richard E. Smalley and Robert F. Curl Jr. of Rice University in Houston, was the Buckminsterfullerene molecule, a cage of 60 carbon atoms made of interlocking pentagons and hexagons.
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Its folding, hivelike design is formed by 18 lightweight beryllium hexagons that work as one; to sharpen focus, 126 small motors pivot these segments in increments as small as one ten-thousandth the width of a grain of lily pollen.
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" Per a press release, engineers spent seven years developing the LELO HEX condoms, which integrate 350 hexagons throughout the inside for what inventor-founder Filip Sedic boasts is a "lightweight and incredibly strong" prophylactic that reduces "the chances of slippage.
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The walls are outfitted with Cloud Island Wire Wall Storage Hexagons in mint ($30) — stuffed full with fun animal plushes also from Cloud Island — as well as critter artwork, like the Cloud Island Wall Canvas Giraffe in neutral gray ($30).
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One lacy spider web was laser-cut from wool; another knitted in micro-pleats from steel and wool to create a dense, swirling exoskeleton; another composed of glistening 3-D printed, transparent laser-cut hexagons (5,000 of them) as airy and alluring as soap bubbles.
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The project has turned into a viral sensation, with people using #RitasQuilt to track progressMore than 1,000 people volunteered, she said, but she chose 100 to embroider the hexagons Rita had left behind — 50 for each state, and another 50 to each stitch a star.
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In the black paintings, each bearing the name of a person, including one titled "Bridget (Bardot)" (2017), Hall might fill in some of the hexagons created by the pattern of dots with dark red oxide, or draw lines connecting the dots to make a schematic rectangle.
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Several of the crafters told The Washington Post that they expected their hexagons to take hours to finish — the woman embroidering her home state of Maine said she expects it to take 20 hours, while the woman working on Alabama said it'll likely take between five and 10 hours.
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Among the spaces is a 4,000-seat multipurpose amplified concert hall in black that transforms itself into a standing-room site to accommodate up to 6,000, and a more intimate 1,500-seat auditorium, whose walls are made of woven oak and its ceiling of wooden hexagons filled with fireproof paper tubes.
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The Hexagon program is part of a legacy of American spies in the sky stretching from the 1950s to today, aimed at finding early warning signs about potential threats to the US. Read the National Reconnaissance Office's declassified file on Hexagon The US National Reconnaissance Office launched 20 Hexagons between 1971 and 223.
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Patricia Thiel, a chemistry and materials science expert based at Iowa State University, used this helpful analogy of tiling a floor to explain the unique properties of quasicrystals in this NPR article: "If you want to cover your bathroom floor, your tiles can be rectangles or triangles or squares or hexagons," she said.
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Braised rabbit leg is a very Prune thing to cook, but I doubt that in 1999 it would have been presented, as it was earlier this summer, over yellow hexagons of carrot mixed with Calabrian chiles, mint leaves and pine nuts, with a handful of fried bread crumbs thrown over the top.
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If you stack two sheets on top of one another and slowly twist one sheet, the hexagons begin to form Moire patterns, larger-scale patterns based on the overlapping spaces, like this:A small twist, or as the researchers call it, a "magic" angle of around 1.1 degrees, essentially confuses the system into thinking that each unit hexagon is much larger.
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He classified the possible patterns on the surface of an Adidas Telstar soccer ball, i.e. specialThe sides of the pentagons may only encounter hexagons; the hexagons must alternately bifurcate with pentagons and hexagons. tilings with pentagons and hexagons on the sphere.Kolumne Mathematische Unterhaltungen, Spektrum der Wissenschaft, Juli 2006Braungardt, Kotschick Die Klassifikation von Fußballmustern, Math.
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Orthogonal projection of a cantor cube showing a hexaflake. A hexaflake is a fractal constructed by iteratively exchanging hexagons by a flake of seven hexagons;. it is a special case of the n-flake. The hexaflake has 7n−1 hexagons in its nth iteration, each smaller by 1/3 than the hexagons in the previous iteration.
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Fractal's gameplay revolves around pushing hexagons into seven-hexagon clusters, or "blooms", which earn the player points. Fractal features three gameplay modes, campaign, arcade, and puzzle. In campaign mode, the player progresses by earning enough points to clear each level. Over the course of the thirty-level campaign, the player encounters different kinds of power-up hexagons with special abilities (hexagons that cause explosions, or that destroy all adjacent hexagons) that help the player earn points.
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411, completely characterizing which numbers of hexagons are possible in a fullerene.
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Therefore, ring can be overlapped by a set of hexagons instead of one. JWST telescope array consists from 18 hexagons. Sampling on 18 shifted lattices is possible for 2-d Fourier transform of the array signal (i. e. for emitted signal).
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Acrylic on Masonite. Hexagons, Number 1, 1984. Cotton. Hermetic Indecision, 1977. Acrylic on Masonite.
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Similarly, the company also manufactures drill bits for other angular holes such as pentagons and hexagons.
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Walls of basalt columns exist in other places in the Golan Heights, along the Meshushim (Hexagons) and Zavitan Rivers.
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The interior star beam (which supports the flèche above, and has cutout hexagons) is 17m (55ft) above the sanctuary.
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Hexagons marked "ZOC" are the zone of control for the combat unit shown in the center (for a wargame that uses hexagons). In board wargames, a zone of control (ZOC) is the area directly adjacent to certain combat forces that affects the movement and actions of enemy combat units. In hexagonal tiled maps, a combat unit's zone of control is the six hexagons adjacent to the hexagon occupied by a unit. The effects of zones of control can vary significantly between different wargame rules.
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A clathrin cage with a single triskelion highlighted in blue. CryoEM map EMD_5119 was rendered in UCSF Chimera and one clathrin triskelion was highlighted. Each cage has 12 pentagons. Mini-coat (left) has 4 hexagons and tetrahedral symmetry as in a truncated triakis tetrahedron. Hexagonal barrel (middle) has 8 hexagons and D6 symmetry.
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The solo player still played white hexagons. The Gold Run used a blue background in this version and the Liza Tarbuck version.
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Graphene consists of one-atom-thick layers of carbon atoms arranged in two-dimensional hexagons,Palmer, Jason. "Bendy gadget future for graphene".
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"Hexagons" is a 2003 alternate history short story by American writer Robert Reed. It was first published in the magazine Asimov's Science Fiction.
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Even smaller cages with zero hexagons probably do not form from the native protein, because the feet of the triskelia are too bulky.
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This is to say that the hexagons H and T^2(H) are equivalent by a label- preserving projective transformation. More precisely, the hexagons H' and T(H) are projectively equivalent, where H' is the labeled hexagon obtained from H by shifting the labels by 3. See the figure. It seems entirely possible that this fact was also known in the 19th century.
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At the end of the game the players count their scores. A "star" is a group of connected stones belonging to one player that touches at least three partial edge hexagons. The score of a star is the number of edge hexagons it touches minus two. A player's score is the total of all the stars of that player's color.
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The game is played on a paper map with 518 one-inch hexagons using die-cut pasteboard counters representing various magical and non-magical units.
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The pentagram map is the identity on the moduli space of pentagons. This is to say that there is always a projective transformation carrying a pentagon to its image under the pentagram map. The map T^2 is the identity on the space of labeled hexagons. Here T is the second iterate of the pentagram map, which acts naturally on labeled hexagons, as described above.
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In geometry, the hexagonal tiling or hexagonal tessellation is a regular tiling of the Euclidean plane, in which three hexagons meet at each vertex. It has Schläfli symbol of {6,3} or t{3,6} (as a truncated triangular tiling). English mathematician John Conway called it a hextille. The internal angle of the hexagon is 120 degrees so three hexagons at a point make a full 360 degrees.
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The tortoise is a favored motif by netsuke-carvers and other artisans, and is featured in traditional Japanese wedding ceremonies. There is also a well-known artistic pattern based on the nearly hexagonal shape of a tortoise's shell. These patterns are usually composed of symmetrical hexagons, sometimes with smaller hexagons within them.Niwa, Motoji, 2001, trans, Thomas, Jay W., Snow, Wave, Pine: Traditional Patterns in Japanese Design, .
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From this it can be seen that a triangle with a vertex at the center of the regular hexagon and sharing one side with the hexagon is equilateral, and that the regular hexagon can be partitioned into six equilateral triangles. Like squares and equilateral triangles, regular hexagons fit together without any gaps to tile the plane (three hexagons meeting at every vertex), and so are useful for constructing tessellations. The cells of a beehive honeycomb are hexagonal for this reason and because the shape makes efficient use of space and building materials. The Voronoi diagram of a regular triangular lattice is the honeycomb tessellation of hexagons.
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The original 1983–86 title sequence featured flipping hexagons with various images on them running down an encyclopedia page. The title sequence used from 1987 to 1994 is a city, paying homage to science-fiction films such as Metropolis (1927) and Blade Runner (1982). In the 1994 Sky series the opening titles were cut short, not featuring the hexagons flying over the studio like the 1987–93 titles. The title sequence used in the 1997 series with a complete different theme tune (although as mentioned above, it might have been similar to the original theme but with several notes swapped around) featured a golden head with hexagons showing clips.
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The 40 non-snub triangular faces form 20 coplanar pairs, forming star hexagons that are not quite regular. Unlike most snub polyhedra, it has reflection symmetries.
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Slay is a hexagonal strategy game where the goal is to conquer the island by buying soldiers and peasants and using them to capture enemies' hexagons.
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No such results are known without making any further assumptions for generalized hexagons or octagons, even for the smallest case of three points on each line.
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If a piece moves onto the outer ring of hexagons, it must move back toward the center on the next turn unless blocked from doing so.
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This breaks the symmetry of the system, and generally changes the pattern of up- and down-moving fluid from stripes to hexagons, as seen at right. Such hexagons are one example of a convection cell. As the Rayleigh number is increased even further above the value where convection cells first appear, the system may undergo other bifurcations, and other more complex patterns, such as spirals, may begin to appear.
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Illuminated by windows hidden from a viewer below, interlocking octagons, crosses and hexagons diminish in size as the dome rises to a lantern with the symbol of the Trinity.
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The solo player attempted to complete a vertical connection of white hexagons from the top of the board to the bottom; that required at least four correct answers. The pair attempted to connect a path from left to right with blue hexagons (purple during the Aspel era), requiring at least five spaces. The first side to connect their path won the game. The first player or team to win two games won the match.
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300px The action of the pentagram map on pentagons and hexagons is similar in spirit to classical configuration theorems in projective geometry such as Pascal's theorem, Desargues's theorem and others.
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Many viral capsids are formed by hexameric and pentameric proteins.Virus Capsid Model Such capsids are assigned a triangulation number (T-number) which describe relation between the number of pentagons and hexagons.
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Interpreting each brick face as a hexagon having two interior angles of 180 degrees allows the pattern to be considered as a proper tiling. However, not all geometers accept such hexagons.
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Havannah is game based on Hex. It differs from Hex in that it is played on a hexagonal grid of hexagons and a win is achieved by forming one of three patterns.
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In geometry, the truncated order-8 triangular tiling is a semiregular tiling of the hyperbolic plane. There are two hexagons and one octagon on each vertex. It has Schläfli symbol of t{3,8}.
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A similar method can be used to subdivide squares into four congruent non-convex pentagons, or regular hexagons into six congruent non-convex pentagons, and then tile the plane with the resulting unit.
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Edge-truncation is a beveling, or chamfer for polyhedra, similar to cantellation, but retaining the original vertices, and replacing edges by hexagons. In 4-polytopes, edge-truncation replaces edges with elongated bipyramid cells.
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On each player's turn, the player moves one of his/her penguins in a straight line as far as he/she wishes, as long as there is a continuous line of vacant hexagons between the penguin's starting and destination hexagons. Penguins can't jump over empty space or other penguins. The hexagon that the penguin started from is then removed from play, becoming the player's property. A penguin that can't move anywhere is removed from play, along with the hexagon it is standing on.
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Clathrin cannot bind to membrane or cargo directly and instead uses adaptor proteins to do this. This triskelion will bind to other membrane-attached triskelia to form a rounded lattice of hexagons and pentagons, reminiscent of the panels on a soccer ball, that pulls the membrane into a bud. By constructing different combinations of 5-sided and 6-sided rings, vesicles of different sizes may assemble. The smallest clathrin cage commonly imaged, called a mini-coat, has 12 pentagons and only two hexagons.
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Old symbol of CDU The present symbol of CDU shows the PCP's symbol and the PEV's symbol, a hammer and sickle and a sunflower, respectively, with the respective names below. That symbol replaced a former one that featured three hexagons with the inscription: CDU and was often used with a beehive. That was sometimes said to mean that CDU worked just like a bee (collectively and every day) and the hexagons were meant to represent the cell-based Leninist organization of the PCP.
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This yields a coarse-resolution equal area grid called the resolution 1 grid. It consists of 20 hexagons on the surface of the sphere and 12 pentagons centered on the 12 vertices of the icosahedron.
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Hexagons Pool Hexagons Pool The Hexagon Pool (, Breichat HaMeshushim) is a natural pool in the Meshushim Reserve, part of the Yehudiya Forest Nature Reserve, in the central Golan Heights. The pool, at the bottom of a canyon, is named after the shape of the hexagonal basalt columns that make up its walls. This geological formation was created by the slow cooling of layers of lava flows over a long period. When the lava solidified and cooled, it was split into polygonal shapes due to its contraction.
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There are many possible generalizations of the cellular automaton concept. A cellular automaton based on hexagonal cells instead of squares (rule 34/2) An example of the Combinations cellular automata creating the Sierpiński triangle One way is by using something other than a rectangular (cubic, etc.) grid. For example, if a plane is tiled with regular hexagons, those hexagons could be used as cells. In many cases the resulting cellular automata are equivalent to those with rectangular grids with specially designed neighborhoods and rules.
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3D model of a rhombicosahedron In geometry, the rhombicosahedron is a nonconvex uniform polyhedron, indexed as U56. It has 50 faces (30 squares and 20 hexagons), 120 edges and 60 vertices. Its vertex figure is an antiparallelogram.
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It is used to design patterns with 6- and 12-pointed stars as well as hexagons in the style called girih. The resulting patterns however characteristically conceal the construction grid, presenting instead a design of interlaced strapwork.
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The Geography and Planning building is located next to Weston Park opposite Bartolomé House. It was designed as a cluster of hexagons in 1960, and is home to the departments of Geography, and Urban Studies and Planning.
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Similar patterns are arranged in diagonal rows: Hexagons with plain, or hooked outlines; squares filled with stars, with interposed kufic-like ornaments; hexagons in diamonds composed of rhomboids, rhomboids filed with stylized flowers and leaves. Their main borders often contain kufic ornaments. The corners are not “resolved”, which means that the border design is cut off, and does not continue around the corners. The colours (blue, red, green, to a lesser extent also white, brown, yellow) are subdued, frequently two shades of the same colour are opposed to each other.
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The board consisted of a pattern of hexagons similar to that of the main game, but the hexagons had 2 to 5 letters inside them; those letters were the initials of the correct answer. (For instance, if a contestant chose "BS" and the host said "Where people kiss in Ireland", the correct answer would be "Blarney Stone.") If a contestant guessed correctly, the hexagon turned gold. However, if the contestant guessed incorrectly or passed, it turned black, blocking the player's path; it was then up to the contestant to work around it.
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3D model of a cubitruncated cuboctahedron In geometry, the cubitruncated cuboctahedron or cuboctatruncated cuboctahedron is a nonconvex uniform polyhedron, indexed as U16. It has 20 faces (8 hexagons, 6 octagons, and 6 octagrams), 72 edges, and 48 vertices.
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Units cannot change facing, which has an important impact on gameplay, as certain attacks can only be performed in one direction. Like other turn-based strategy games, the playing field is also divided into hexagons with varying effects.
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3D model of a small icosicosidodecahedron In geometry, the small icosicosidodecahedron (or small icosified icosidodecahedron) is a nonconvex uniform polyhedron, indexed as U31. It has 52 faces (20 triangles, 12 pentagrams, and 20 hexagons), 120 edges, and 60 vertices.
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For space-filling, the triakis truncated tetrahedron can be constructed as follows: # Truncate a regular tetrahedron such that the big faces are regular hexagons. # Add an extra vertex at the center of each of the four smaller tetrahedra that were removed.
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The leaf margin is crenulate (finely scalloped) to regular serrulate (sawlike). The marginal cells are often thinner with thicker cell walls. There are about 2-3 cells in the costa. The leaf cells are very turgid and irregularly round-like hexagons.
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The Hexagon VLIW The Hexagon is a 4-issue VLIW. Qualcomm Announces Its 2012 Superchip: 28nm Snapdragon S4, 10/12/2011 by John Oram. The article states that Hexagons have been in Snapdragon chips since 2006. Estimate of Snapdragon volumes.
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First, flat multi- layered sheets are produced combining plastic, coloring, and reflective material such as aluminium, titanium dioxide, iron oxide, and bismuth oxychloride. These sheets are then cut into tiny particles of many shapes including squares, triangles, rectangles, and hexagons.
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This four story building contains mostly classrooms, which are shaped in hexagons instead of rectangles. The design considerations include making the students feel less crowded and allowing the students at the side to view the blackboard with a smaller angle.
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The blue-and-white tiles on the wall are arranged in hexagons and triangles in the Bursa manner.Davis, pg. 267 Some show delicate patterns of flowers, leaves, clouds or other abstract forms. The white plasterwork is in the Persian manner.
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Adamus, P.R., K. Larsen, G. Gillson, and C. Miller. 2001. Oregon Breeding Bird Atlas. Oregon Field Ornithologists, Eugene, OR. CD-ROM. . The hexagons, each with an area of 435 square kilometers, also contained a survey unit of 25 square kilometers.
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The winner of the match went on to play the Gold Run bonus round; if the pair won, only one player on the team could play, with the turns alternating at each Gold Run. The board consisted of a pattern of green hexagons similar to that of the main game, but the hexagons had 2 to 4 letters inside them; those letters were the initials of the correct answer. (For instance, if a contestant chose "BS" and the host said "Where people kiss in Ireland", the correct answer would be "Blarney Stone.") When the contestant guessed correctly, the hexagon turned gold.
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Using these theorems he derived explicit formulas for triangles and tetragons and also gave formulas for pentagons, hexagons, and heptagons. He also presented a classification of problems for tetragons, pentagons, and hexagons. For the second group of problems, Lexell showed that their solutions can be reduced to a few general rules and presented a classification of these problems, solving the corresponding combinatorial problems. In the second article he applied his general method for specific tetragons and showed how to apply his method to a polygon with any number of sides, taking a pentagon as an example.
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The Giant's Causeway, in Northern Ireland Polygons appear in rock formations, most commonly as the flat facets of crystals, where the angles between the sides depend on the type of mineral from which the crystal is made. Regular hexagons can occur when the cooling of lava forms areas of tightly packed columns of basalt, which may be seen at the Giant's Causeway in Northern Ireland, or at the Devil's Postpile in California. In biology, the surface of the wax honeycomb made by bees is an array of hexagons, and the sides and base of each cell are also polygons.
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Based on Dota Auto Chess, a mod for Dota 2, the game centers around eight players who construct teams to fight one another and be the last player standing. The battlefield consists of hexagons, where players can strategically place units on the hexagons on their side of the game board between rounds. Each round, a short battle automatically commences, with two players matched randomly for that round, or else paired against computer-controlled enemies. In the rounds against computer-controlled enemies, each enemy has a chance to drop gold, units, or items that the player can use.
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It was unique as a self-contained printed product for the commercial market not requiring miniatures or building a map. Tactics II is a revised version published by Avalon Hill in 1958, then reissued in 1961 and 1973. It uses hexagons instead of squares, after Roberts saw a picture of a RAND game Life magazine that used hexagons which he believed would provide more realistic movement. In 1972, the game was discontinued due to rising costs, but was redesigned in 1973 with less costly components and used as a loss leader as it was an introductory wargame.
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3D model of a small dodecicosahedron In geometry, the small dodecicosahedron (or small dodekicosahedron) is a nonconvex uniform polyhedron, indexed as U50. It has 32 faces (20 hexagons and 12 decagons), 120 edges, and 60 vertices. Its vertex figure is a crossed quadrilateral.
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3D model of an icosidodecadodecahedron In geometry, the icosidodecadodecahedron (or icosified dodecadodecahedron) is a nonconvex uniform polyhedron, indexed as U44. It has 44 faces (12 pentagons, 12 pentagrams and 20 hexagons), 120 edges and 60 vertices. Its vertex figure is a crossed quadrilateral.
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Also, any completely isolated areas that don't have any penguins on them are removed from play. When none of the penguins are in play any more, the game ends. The player who has collected the most fish from his/her hexagons wins.
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There are blockfields present around where the ground has cracked to form hexagons. Solifluction occurs when the night temperatures freeze the soil before it thaws again in the morning. This daily expansion and contraction of the soil prevents the establishment of vegetation.
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The order date of 1554, the price remains unknown. Achieving the woodwork necessitated six months of work only. The coffered ceiling, pegged, is considered one of the finest in France. It consists of a large octagon surrounded by eight small hexagons finely carved.
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The advantage of pattern block art is that it can be changed around, added, or turned into something else. All six of the shapes (green triangles, blue (thick) rhombi, red trapezoids, yellow hexagons, orange squares, and tan (thin) rhombi) are applied to make mosaics.
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Cycle graph The four hexagonal cycles have the inversion (the black knot on top) in common. The hexagons are symmetric, so e.g. 3 and 4 are in the same cycle. A regular octahedron has 24 rotational (or orientation-preserving) symmetries, and 48 symmetries altogether.
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Because the three- dimensional shape of Namacalathus is complex, and the wall is so thin, the fossils appear as a two-dimensional sections in a wide variety of shapes, including closed and open circles, irregular hexagons or heptagons, as well as heart and moon shapes.
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The prismatic pentagonal tiling is a dual uniform tiling in the Euclidean plane. It is one of 15 known isohedral pentagon tilings. It can be seen as a stretched hexagonal tiling with a set of parallel bisecting lines through the hexagons. Conway calls it an .
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The Battle for Wesnoth, a hex grid based computer game A hex map, hex board, or hex grid is a game board design commonly used in wargames of all scales. The map is subdivided into a hexagonal tiling, small regular hexagons of identical size.
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As a result, defending an edge against a center attack is very difficult. Schensted and Titus attacked this problem with successive versions of the game board, culminating in the present "official" board with three pentagons inserted among the hexagons. They noted that were players to play on a hemisphere rather than a plane with hexagons, with the equator divided into three "sides" (each 1/3 the circumference of the hemisphere), the distance from the "north pole" of the hemisphere to the equator was 1/4 the circumference, and thus the distance ratio improved from 1/3 to 3/4. This made defending a side from a center attack much more plausible.
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Although theorists had speculated about the existence and possible properties of free-standing silicene, researchers first observed silicon structures that were suggestive of silicene in 2010. Using a scanning tunneling microscope they studied self-assembled silicene nanoribbons and silicene sheets deposited onto a silver crystal, Ag(110) and Ag(111), with atomic resolution. The images revealed hexagons in a honeycomb structure similar to that of graphene, which, however, were shown to originate from the silver surface mimicking the hexagons. Density functional theory (DFT) calculations showed that silicon atoms tend to form such honeycomb structures on silver, and adopt a slight curvature that makes the graphene-like configuration more likely.
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3D model of a great icosicosidodecahedron In geometry, the great icosicosidodecahedron (or great icosified icosidodecahedron) is a nonconvex uniform polyhedron, indexed as U48. It has 52 faces (20 triangles, 12 pentagrams, and 20 hexagons), 120 edges, and 60 vertices. Its vertex figure is a crossed quadrilateral.
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Fractal: Make Blooms Not War is a puzzle video game by Cipher Prime. The game involves pushing hexagonal fragments together to form large hexagons and chain reactions. Fractal was released by Cipher Prime via their website on May 26, 2010 for OS X and Microsoft Windows.
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Moufang 6-gons are also called Moufang hexagons. A classification of Moufang 6-gons was stated by Tits,J. Tits, Classification of buildings of spherical type and Moufang polygons: a survey, in Coll. Internaz. Teorie Combinatorie, Atti dei Convegni Lincei 17, Rome 1976, pp. 229–246.
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Defeating a pentagon, for example, requires five players to hit the five points of the shape simultaneously in order to destroy it. Destroying the hexagons earns the players blocks, which can be used to build engines or silos, the latter of which can capture more blocks.
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For example, Hemiselmis pacifica possesses Cr-PC577, and Cr-PC612 is found in Hemiselmis virescens and Hemiselmis tepida. The chloroplasts are red in color. The species has periplast surrounding the cells below plasma membrane. The periplast consists of internal and superficial plates that have a general shape of hexagons.
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Soccer ball (right) has 20 hexagons and icosahedral symmetry as in a truncated icosahedron. Mechanism of clathrin-mediated endocytosis. The clathrin triskelion is composed of three clathrin heavy chains interacting at their C-termini, each ~190 kDa heavy chain has a ~25 kDa light chain tightly bound to it.
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The metal fasteners, joints, and internal steel frames remain dry, preventing frost and corrosion damage. The concrete resists sun and weathering. Some form of internal flashing or caulking must be placed over the joints to prevent drafts. The 1963 Cinerama Dome was built from precast concrete hexagons and pentagons.
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3, p. 171 (topological equivalence of trihexagonal and two-triangle tilings). It consists of equilateral triangles and regular hexagons, arranged so that each hexagon is surrounded by triangles and vice versa. The name derives from the fact that it combines a regular hexagonal tiling and a regular triangular tiling.
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The gameplay is similar to "Flow Free" except the layout resembles hexagons instead of squares. The third expansion, "Flow Free: Warps", was released on August 8, 2017. This expansion allows you to have pipes warp from the edge of the map to the other edge of the map.
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After another eighteen seconds and eighteen hexagons have elapsed, the time expires and Bruce offers the hive to the other team, who may earn a bonus point by answering the grid. Once each team has cleared two hives each, they have to find two related answers from the same hive.
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The community's arms show a stylized representation of Saint Kilian’s Church above. The seven hexagons symbolize the basalt columns found in the area around the Hausberg Bornkasten. Below, the former drinking water supply is symbolized as a well. The wavy bendlet stands for the Eisenbach, which flows through the community.
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Cyclopropanation (the Bingel reaction) is another common method for functionalizing C60. Cyclopropanation of C60 mostly occurs at the junction of 2 hexagons due to steric factors. The first cyclopropanation was carried out by treating the β-bromomalonate with C60 in the presence of a base. Cyclopropanation also occur readily with diazomethanes.
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Each type of terrain has its own bonuses for offense, defense, and movement. A typical mission in a campaign lasts for at least 27 turns per side and wind levels come in five degrees of severity. The board is divided into multiple hexagons like in similar turn-based strategy games.
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A mikoshi in Jak Japan Matsuri 2018 Woman mikoshi Children mikoshi (Sanja Matsuri) Japan's largest (Tomioka Hachiman Shrine) Utagawa Hirokage Typical shapes are rectangles, hexagons, and octagons. The body, which stands on two or four poles (for carrying), is usually lavishly decorated, and the roof might hold a carving of a phoenix.
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Graphyne-n varieties, where n indicates the number of carbon-carbon triple bonds in a link between two adjacent hexagons. Graphyne is graphyne-1; graphdiyne is graphyne-2. Graphyne is an allotrope of carbon. Its structure is one-atom-thick planar sheets of sp and sp2-bonded carbon atoms arranged in crystal lattice.
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BBC Two used adult contestants, instead of sixth formers. This version was broadcast in 1997 and presented by Michael Aspel; the show stayed with the same format. Famous contestants included Stephen Merchant. This is the only version to use purple hexagons; all other versions still used blue to represent the pair of players.
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The buckyballs are released into a helium or hydrogen gas, which expands at supersonic speeds, carrying the carbon balls with it. The buckyballs achieve energies of around 40 keV without changing their internal dynamics. This material contains hexagons and pentagons that come from the original structures. The pentagons could introduce a band gap.
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Single player Tournament mode. The green cubes are the pick-up icons and the purple hexagons are speed boost tokens. Speed Freaks is a kart racing game featuring several single and multiplayer modes. During the game, players take control of one of nine characters and drive karts around tracks with various themes.
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Buckminsterfullerene is a type of fullerene with the formula C60. It has a cage-like fused-ring structure (truncated icosahedron) that resembles a soccer ball, made of twenty hexagons and twelve pentagons. Each carbon atom has three bonds. It is a black solid that dissolves in hydrocarbon solvents to produce a violet solution.
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These 12 order-5 vertices can be truncated such that all edges are equal length. The original 30 rhombic faces become non-regular hexagons, and the truncated vertices become regular pentagons. The hexagon faces can be equilateral but not regular with D2 symmetry. The angles at the two vertices with vertex configuration 6.6.
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Reaction–diffusion systems have attracted much interest as a prototype model for pattern formation. Patterns such as fronts, spirals, targets, hexagons, stripes and dissipative solitons are found in various types of reaction- diffusion systems in spite of large discrepancies e.g. in the local reaction terms. Such patterns have been dubbed "Turing patterns".
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3D model of an octahemioctahedron In geometry, the octahemioctahedron or allelotetratetrahedron is a nonconvex uniform polyhedron, indexed as U3. It has 12 faces (8 triangles and 4 hexagons), 24 edges and 12 vertices. Its vertex figure is a crossed quadrilateral. It is one of nine hemipolyhedra, with 4 hexagonal faces passing through the model center.
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3D model of a truncated great icosahedron In geometry, the truncated great icosahedron (or great truncated icosahedron) is a nonconvex uniform polyhedron, indexed as U55. It has 32 faces (12 pentagrams and 20 hexagons), 90 edges, and 60 vertices. It is given a Schläfli symbol t{3,} or t0,1{3,} as a truncated great icosahedron.
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The nucleus to nucleus diameter of a buckminsterfullerene molecule is about 0.71 nm. The buckminsterfullerene molecule has two bond lengths. The 6:6 ring bonds (between two hexagons) can be considered "double bonds" and are shorter than the 6:5 bonds (between a hexagon and a pentagon). Its average bond length is 1.4 angstroms.
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LoPresti, 1996 OMR systems approach one hundred percent accuracy and only take 5 milliseconds on average to recognize marks. Users can use squares, circles, ellipses and hexagons for the mark zone. The software can then be set to recognize filled in bubbles, crosses or check marks. OMR can also be used for personal use.
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The game provides the atmosphere of the island of Java on a hexagonal board. Players build the island and score by setting up palace festivals at opportune moments. When players run out of hexagons to build the island, the game is over. A final scoring phase now takes place and a winner is declared.
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Phares, Heather "Violet Cries Review", Allmusic. Retrieved 24 March 2013 NME said it was "gothic but not goth" giving it 8/10. After the release of the album they went on to release two more singles off the album, "Warpath" and "Chorea". In November 2011 they released the Hexagons EP as a digital download.
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The game of Y is Hex played on a triangular grid of hexagons; the object is for either player to connect all three sides of the triangle. Y is a generalization of Hex to the extent that any position on a Hex board can be represented as an equivalent position on a larger Y board.
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3D model of a dodecadodecahedron In geometry, the dodecadodecahedron is a nonconvex uniform polyhedron, indexed as U36. It is the rectification of the great dodecahedron (and that of its dual, the small stellated dodecahedron). It was discovered independently by , and . The edges of this model form 10 central hexagons, and these, projected onto a sphere, become 10 great circles.
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3D model of a small dodecahemicosahedron In geometry, the small dodecahemicosahedron (or great dodecahemiicosahedron) is a nonconvex uniform polyhedron, indexed as U62. It has 22 faces (12 pentagrams and 10 hexagons), 60 edges, and 30 vertices. Its vertex figure is a crossed quadrilateral. It is a hemipolyhedron with ten hexagonal faces passing through the model center.
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3D model of a great dodecahemicosahedron In geometry, the great dodecahemicosahedron (or small dodecahemiicosahedron) is a nonconvex uniform polyhedron, indexed as U65. It has 22 faces (12 pentagons and 10 hexagons), 60 edges, and 30 vertices. Its vertex figure is a crossed quadrilateral. It is a hemipolyhedron with ten hexagonal faces passing through the model center.
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3D model of a great truncated icosidodecahedron In geometry, the great truncated icosidodecahedron (or great quasitruncated icosidodecahedron or stellatruncated icosidodecahedron) is a nonconvex uniform polyhedron, indexed as U68. It has 62 faces (30 squares, 20 hexagons, and 12 decagrams), 180 edges, and 120 vertices. It is given a Schläfli symbol t0,1,2{,3}, and Coxeter-Dynkin diagram, .
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First is prominent use of repeated patterns of geometric shapes, such as circles, squares, diamonds, and hexagons, which can be seen in the garb of some of Buddha's royal disciples. The second similarity is striped patterns, especially around deities' legs. Finally, textiles seen in the temple's murals use the motif of scrolls extended like arabesques into repeated circles.
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Daisenryaku Portable is a military turn-based strategy game for the PlayStation Portable published by Genki. It was followed by Daisenryaku Portable 2 in 2006. The game takes place on a battle field of hexagons, upon which the player assembles an army. The aim is to capture cities and factories, in order to increase available resources.
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Architects, P.C. The South Tower is the tallest, reaching with 34 floors, while the North Tower is tall with 23 floors. The two towers are elongated hexagons made of silver grey aluminum panels contrasted by dark grey reflective glass. They sit diagonally from one another, connected by a six- story terraced building. At street level is a retail mall.
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The Mountain Loop also includes the aforementioned Overlook Picnic Area. Quarry Trail: A trail, blazed with blue hexagons, takes hikers around the edge of the Morrow Mountain picnic area and into the former quarry. For much of the early 20th century, the area was mined for rocks. Hikers may enjoy the evenly cut paths and the washhouses.
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Geodesic grids may use the dual polyhedron of the geodesic polyhedron, which is the Goldberg polyhedron. Goldberg polyhedra are made up of hexagons and (if based on the icosahedron) 12 pentagons. One implementation that uses an icosahedron as the base polyhedron, hexagonal cells, and the Snyder equal-area projection is known as the Icosahedron Snyder Equal Area (ISEA) grid.
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Many patterns exist, while the quilting block is one that is widely used. Other patterns include the Chinese coin, 100 good wishes and lattice. Some may include squares, triangles, hexagons and diamonds. Traditional culture and folk legends are often the themes for patchworks, such as the Qilin Bringing the Child, Door Gods, the Dragon King and the Kitchen God.
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He reduced all of the current knowledge into a linked set of differential equations. Figure of Maxwell's molecular vortex model. For a uniform magnetic field, the field lines point outward from the display screen, as can be observed from the black dots in the middle of the hexagons. The vortex of each hexagonal molecule rotates counter-clockwise.
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Holdridge life zone classification scheme. Although conceived as three- dimensional by its originator, it is usually shown as a two-dimensional array of hexagons in a triangular frame. The Holdridge life zones system is a global bioclimatic scheme for the classification of land areas. It was first published by Leslie Holdridge in 1947, and updated in 1967.
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During combat, the field is split into seven hexagonal sections, some of which may have special properties. The player and enemies can move to different hexagons during their turn. This time around, the party count is three instead of four. Dean's party members and enemies can act instantly when they move onto the next hexagonal platform.
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When either party was one correct answer away from completing their path, the hexagons forming their path would flash to indicate this. If both were one correct answer away, all lit hexagons on the board would flash, indicating that the situation was effectively "Blockbusters either way" (later referred to as a "mutual space" on the board), and the next player to give a correct answer would win the game, unless the contestant chose a panel which would not give them the win, which was sometimes used as a safety tactic to avoid handing the initiative to the opponent in case they gave the wrong answer. All players received a "Blockbusters" Concise Oxford Dictionary and sweatshirt in the original ITV series. By 1985, the Blockbusters computer game was added.
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Convex polygons are star shaped, and a convex polygon coincides with its own kernel. Regular star polygons are star-shaped, with their center always in the kernel. Antiparallelograms and self-intersecting Lemoine hexagons are star- shaped, with the kernel consisting of a single point. Visibility polygons are star-shaped as every point within them must be visible to the center by definition.
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The game included rules for leadership, snipers, civilians, helicopter travel, artillery, and air strikes. The map was 22" x 28" printed in black and tan, and included counters, a rule booklet, as well as game charts and tables. The map was divided into hexagons at a scale 100 yards per hex. Grunt was later redesigned and released as Search & Destroy.
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In 2000, parts of the defensive wall and two round towers were reconstructed on original foundations of the walls. On the remains of the old military station on the hilltop, which had underfloor heating in the form of a hypocaust, a protective structure was built. All roofs were covered in slates in the form of scales and hexagons (for protection).
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Overall these and other detail changes made the cars much plainer, and certainly lost the model some of its charm. In the U.S. the 1976 rear lights were hexagons. The 1977 rear lights were rectangular. An optional RX-3 'special appearance package' called the RX-3sp was sold in 1977 to advertise the new 75,000 mile engine guarantee for rotary engines.
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Tropical Reef Research. This species has a long dorsal fin with eleven spines, 15-17 dorsal soft rays and 8 anal soft rays. The body is ochre to light brown, stocky, with an oval profile. It is covered by small brown hexagons with pale interspaces disposed on irregular darker diagonal bands and forming a network (hence the common name of the species).
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Another interpretation can represent this solid as a hexahedron, by considering pairs of trapezoids as a folded regular hexagon. It will have 6 faces (4 triangles, and 2 hexagons), 12 edges, and 8 vertices. It could also be seen as a folded tetrahedron also seeing pairs of end triangles as a folded rhombus. It would have 8 vertices, 10 edges, and 4 faces.
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The 6:6 ring bonds (between two hexagons) can be considered "double bonds" and are shorter than the 6:5 bonds (between a hexagon and a pentagon). Its average bond length is 0.14 nm. Each carbon atom in the structure is bonded covalently with 3 others.Katz, 364 Electronic structure of C60 under "ideal" spherical (left) and "real" icosahedral symmetry (right).
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Hexagonal layered polymeric nitrogen (HLP-N) is the third form of polymeric nitrogen found stable under pressure and was experimentally synthesized at 244 GPa and 3300 K. It adopts a tetragonal unit cell (P42bc) in which the single-bonded nitrogen atoms form two layers of interconnected N6 hexagons. It was found to be metastable down to at least 66 GPa.
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Different ice crystals present together in a cloud As the ice crystals grow, they can bump into each other and splinter and fracture, resulting in many new ice crystals. There are many shapes of ice crystals to bump into each other. These shapes include hexagons, cubes, columns, and dendrites. This process is referred to as "ice enhancement" by atmospheric physicists and chemists.
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Star is played on a board of hexagonal spaces. Although the board can have any size and shape, a board with unequal edges is generally used to avoid ties. Players may not place stones on the partial hexagons off the edge of the board; these are used for scoring. One player places black stones on the board; the other player places white stones.
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It is important to remember that triangles are strong in terms of rigidity, but while packed in a tessellating arrangement triangles are not as strong as hexagons under compression (hence the prevalence of hexagonal forms in nature). Tessellated triangles still maintain superior strength for cantilevering however, and this is the basis for one of the strongest man made structures, the tetrahedral truss.
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Gabrielite has a pseudohexagonal shape and the crystal structure is composed of parallel sheets of ditriagonalization of hexagons which reduces it to a P3 symmetry. According to the American Mineralogist, Gabrielite shows a 6-Fold outline.Graeser, S., Topa, D., Balić- Žunić, T., and Makovicky, E. (2006) A New Species of Thallium Sulfosalt from Lengenbach, Binntal, Switzerland. Canadian Mineralogist, 44, 135-140.
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Simple QinQ Example This simple example will illustrate a practical use of 802.1ad. The diagram shows switches as hexagons, and a Service Provider (SP) network encompassing all items within the dotted oval. The items on the periphery of the oval are networks belonging to SP customers. Different physical locations appear in the shaded rectangle, and include both customer and SP network components.
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Hex had an incarnation as the question board from the television game show Blockbusters. In order to play a "move", contestants had to answer a question correctly. The board had 5 alternating columns of 4 hexagons; the solo player could connect top-to-bottom in 4 moves, while the team of two could connect left-to-right in 5 moves.
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Icosahedron This polyhedron can be constructed from an icosahedron with the 12 vertices truncated (cut off) such that one third of each edge is cut off at each of both ends. This creates 12 new pentagon faces, and leaves the original 20 triangle faces as regular hexagons. Thus the length of the edges is one third of that of the original edges.
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This construction is more prone to failure and less easily repaired than traditional materials. Honeycomb radiator tubes An earlier construction method was the honeycomb radiator. Round tubes were swaged into hexagons at their ends, then stacked together and soldered. As they only touched at their ends, this formed what became in effect a solid water tank with many air tubes through it.
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Characters are living 2D shapes such as triangles and hexagons. The game includes rules, three adventures and four adventure outlines, a wargame by Matthew Hartley, a long section on the 'science' of Flatland which attempts to explain aspects of the world and its natives, and the original book. It is sold as a charity project in aid of Médecins Sans Frontières (Doctors Without Borders).
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Retrieved: 2013-10-14. Most modern Association footballs are stitched from 32 panels of waterproofed leather or plastic: 12 regular pentagons and 20 regular hexagons. The 32-panel configuration is the spherical polyhedron corresponding to the truncated icosahedron; it is spherical because the faces bulge from the pressure of the air inside. The first 32-panel ball was marketed by Select in the 1950s in Denmark.
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Among regular polygons, only the triangle and square can be dissected into smaller equally sized copies of themselves. However, a regular hexagon can be dissected into six equilateral triangles, each of which can be dissected into a regular hexagon and three more equilateral triangles. This is the basis for an infinite tiling of the hexagon with hexagons. The hexagon is therefore an irrep-∞ or irrep-infinity irreptile.
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The reticulum (derived from the Latin for net ) is lined with ridges that form a hexagonal honeycomb pattern. The ridges are approximately 0.1–0.2 mm wide and are raised 5 mm above the reticulum wall. The hexagons in the reticulum are approximately 2–5 cm wide in cattle. These features increase the surface area of the reticulorumen wall, facilitating the absorption of volatile fatty acids.
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Two teams of three play the game. For this round, each team faces four hives each; they must find an answer embedded into the hive. They have twenty seconds to find it, and five points are on offer; after two seconds hexagons start disappearing from the hive. Once another two have elapsed, the hive is worth a point less and decreases in value every four seconds.
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Halsey Rodman (born 1973) is an artist based in New York City. Rodman was born in Davis, California. He makes installations containing assemblages, videos, photography, text and figurative sculpture,Roger White, TheBrooklynRail.org which form mythological narratives.Press release for The Navigator’s Quarters Must Not Be Disturbed at Guild & Greyshkul Common motifs in Rodman’s work are hexagons, clouds of smoke, pickles and geometric formsHalsey Rodman Studio Visit FlashArtOnline.
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Renga is a "theatrical co-op" game. It is designed to be played in a movie theater with up to one hundred players, with each player holding a laser pointer. Players must pilot a space ship by hitting one of four arrows, which causes the ship to move. At the same time, players must also defend the ship from objects such as pentagons and hexagons.
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In geometry, the elongated dodecahedron,Coxeter (1973) p.257 extended rhombic dodecahedron, rhombo-hexagonal dodecahedronWilliamson (1979) p169 or hexarhombic dodecahedronFedorov's five parallelohedra in R³ is a convex dodecahedron with 8 rhombic and 4 hexagonal faces. The hexagons can be made equilateral, or regular depending on the shape of the rhombi. It can be seen as constructed from a rhombic dodecahedron elongated by a square prism.
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This energy turns out to be comparable to that of bulk tungsten trioxide and molybdenum trioxide. The photoelectric signal is also broad which suggests a large difference in conformation between the anion and the neutral species. Computational chemistry shows that the anions and dianions are ideal hexagons with identical metal-to-metal bond lengths. The molecules discussed thus far only exist diluted in the gas phase.
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In geometry, the order-7 truncated triangular tiling, sometimes called the hyperbolic soccerball,HOW TO BUILD YOUR OWN HYPERBOLIC SOCCER BALL MODEL is a semiregular tiling of the hyperbolic plane. There are two hexagons and one heptagon on each vertex, forming a pattern similar to a conventional soccer ball (truncated icosahedron) with heptagons in place of pentagons. It has Schläfli symbol of t{3,7}.
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The largest strictly-convex deltahedron is the regular icosahedron This is a truncated tetrahedron with hexagons subdivided into triangles. This figure is not a strictly-convex deltahedron since coplanar faces are not allowed within the definition. In geometry, a deltahedron (plural deltahedra) is a polyhedron whose faces are all equilateral triangles. The name is taken from the Greek upper case delta (Δ), which has the shape of an equilateral triangle.
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The symmetry of a crystal is constrained by the requirement that the unit cells stack perfectly with no gaps. There are 219 possible crystal symmetries, called crystallographic space groups. These are grouped into 7 crystal systems, such as cubic crystal system (where the crystals may form cubes or rectangular boxes, such as halite shown at right) or hexagonal crystal system (where the crystals may form hexagons, such as ordinary water ice).
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With this construction it is given the Wythoff symbol: . 50px A skew cantellation of the tetrahedron produces a solid with faces parallel to those of the cuboctahedron, namely eight triangles of two sizes, and six rectangles. While its edges are unequal, this solid remains vertex-uniform: the solid has the full tetrahedral symmetry group and its vertices are equivalent under that group. The edges of a cuboctahedron form four regular hexagons.
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Therefore, the resulting cone angle should have only certain, discrete values α = 2 arcsin(1 − n/6) = 112.9°, 83.6°, 60.0°, 38.9°, and 19.2° for n = 1, ..., 5, respectively. The graphene sheet is composed solely of carbon hexagons which can not form a continuous cone cap. As in the fullerenes, pentagons have to be added to form a curved cone tip, and their number is correspondingly n = 1, ..., 5.
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The title sequence used in 2000–01 featured people throwing and catching the letters that spell "Blockbusters" using the Ed Welch theme again. The 2012 title sequence features references to all previous title sequences, mainly hexagons - but also with more subtle features like the golden head (as seen in the 1997 BBC version), and the planet Earth and a city-like structure as seen in the popularised 1987–95 versions.
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This panel also gives a depiction of Socrates. Domenico Beccafumi, the most renowned Sienese artist of his time, worked on cartoons for the floor for thirty years (1518–1547). Half of the thirteen Scenes from the Life of Elijah, in the transept of the cathedral, were designed by him (two hexagons and two rhombuses). The eight-meter long frieze Moses Striking water from the Rock was executed by him in 1525.
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The original theory, a reaction–diffusion theory of morphogenesis, has served as an important model in theoretical biology. Reaction–diffusion systems have attracted much interest as a prototype model for pattern formation. Patterns such as fronts, hexagons, spirals, stripes and dissipative solitons are found as solutions of Turing-like reaction–diffusion equations. Turing proposed a model wherein two homogeneously distributed substances (P and S) interact to produce stable patterns during morphogenesis.
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Navy fields were generally built with two runways in a cross, with a third runway intersecting the other two at an angle. There were, of course, other designs, including single-runway fields. Most noteworthy were "landing mats," large concrete squares, hexagons and circles, which allowed takeoffs and landings in any direction. Following the war, many bases and auxiliary fields were given to local governments or returned to service as municipal airports.
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Ashurkhana include sites like the Niyaz Khana (offering place), Naqaar Khana (drums place), Sarai Khana's (rest taking place for devotees) Abdar Khana (drinking water place), Langar Khana (food serving place), Makan-e-Mujawer (Mujawer Residence), Daftar-e-Mujawer (Mujawer office), Alawa Chabutra, and Guardroom. The Ashur Khana stands today with enamel tiles that have retained their lustre and vibrant colours even after four centuries. The intricate design in hexagons is exquisite.
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The object of the game is to be the first to win a set number of Victory Medals, usually 4 to 6, depending on the selected battle scenario's victory conditions. A Victory Medal is gained for each enemy unit entirely eliminated from the battlefield. In some scenarios, additional Medals may be gained from the board map itself, for capturing and holding certain terrain hexagons (hexes) or battlefield objectives.
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Furthermore, the angle of an Isosceles Triangle or the number of sides of a (regular) Polygon may be altered during life by deeds or surgical adjustments. An equilateral triangle is a member of the craftsman class. Squares and Pentagons are the "gentlemen" class, as doctors, lawyers, and other professions. Hexagons are the lowest rank of nobility, all the way up to (near) Circles, who make up the priest class.
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Dome of Jams Mosque YazdGirih patterns are very likely to be all over the walls of some Islamic architectures. The decorating lines connect to each other and form a continuous network across the entire tiling with edges combine together. In addition, girih patterns vary a lot on the surface, with different geometric shapes including decagons, hexagons, bowties and rhombuses. Among all these patterns, a special technique is shared: "self-similar transformation".
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In Hidato, a grid of cells is given. It is usually square-shaped, like Sudoku or Kakuro, but it can also include hexagons or any shape that forms a tessellation. It can have inner holes (like a disc), but it has to be made of only one piece. The goal is to fill the grid with a series of consecutive numbers adjacent to each other vertically, horizontally, or diagonally.
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Reinhardt had previously considered the question of anisohedral convex polygons, showing that there were no anisohedral convex hexagons but being unable to show there were no such convex pentagons, while finding the five types of convex pentagon tiling the plane isohedrally. Kershner gave three types of anisohedral convex pentagon in 1968; one of these tiles using only direct isometries without reflections or glide reflections, so answering a question of Heesch.
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In geometry, the truncated hexagonal tiling is a semiregular tiling of the Euclidean plane. There are 2 dodecagons (12-sides) and one triangle on each vertex. As the name implies this tiling is constructed by a truncation operation applies to a hexagonal tiling, leaving dodecagons in place of the original hexagons, and new triangles at the original vertex locations. It is given an extended Schläfli symbol of t{6,3}.
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Buckminsterfullerene is a truncated icosahedron with 60 vertices and 32 faces (20 hexagons and 12 pentagons where no pentagons share a vertex) with a carbon atom at the vertices of each polygon and a bond along each polygon edge. The van der Waals diameter of a molecule is about 1.01 nanometers (nm). The nucleus to nucleus diameter of a molecule is about 0.71 nm. The molecule has two bond lengths.
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Besides acting as an anti-trawling device, the concrete hexagons/squares also act as artificial reefs and attract bivalves, sponges, barnacles and algae, which then in turn will attract organisms such as oysters and mussels, all of which naturally filters the water and therefore counter the threat of toxic algal blooms. In June 2018, MCC's anti-trawling structures were awarded one of the first three National Geographic Society's Marine Protection Prize.
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Each building contains a lobby and eight additional floors. Each floor contains approximately 25 rooms, most with the capacity to house two students. Each set of two floors share a common "lounge", with the exception of the seventh and eighth floors of the towers, which each have their own. Haggett Hall is unique in that its rooms are in the shapes of hexagons, each with a triangular closet.
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In recent times, reaction–diffusion systems have attracted much interest as a prototype model for pattern formation. The above-mentioned patterns (fronts, spirals, targets, hexagons, stripes and dissipative solitons) can be found in various types of reaction–diffusion systems in spite of large discrepancies e.g. in the local reaction terms. It has also been argued that reaction–diffusion processes are an essential basis for processes connected to morphogenesis in biologyL.
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A typical example is the following. Color each hexagon of the infinite honeycomb lattice black with probability p and white with probability 1-p, independently of each other. Let a, b, c, d be four hexagons, not necessarily distinct. Let a \leftrightarrow b and c\leftrightarrow d be the events that there is a black path from a to b, and a black path from c to d, respectively.
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The ridges are approximately 0.1–0.2 mm wide and are raised 0.5 cm above the reticulum wall. The hexagons in the reticulum are approximately 2–5 cm wide in cattle. Despite the differences in the texture of the lining of the two parts of the reticulorumen, it represents one functional space. Microbial fermentation degrades otherwise indigestible polymers in the reticulorumen to volatile fatty acids (VFAs), methane, and carbon dioxide.
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"Hexagons" was a finalist for the 2004 Hugo Award for Best Novelette.2004 Hugo Awards , at TheHugoAwards.org; retrieved June 14, 2018 Io9 has noted that, unlike many stories in which the Roman Empire did not fall, "Hexagons" is not "explicitly dystopian".Great moments in alternate history: the non-fall of the Roman empire, by David Daw; published June 6, 2010; retrieved June 15, 2018 Tangent Onlines Chris Markwyn considered it to be a "compelling" story that is "well- told but fairly conventional", and observed that the contraband history- simulator owned by Samuel's friend's grandfather "undercut" the story's ability to "assert its own reality"; Markwyn further noted that Reed's choice of villain — a "blue-eyed, small-mustached, table-pounding ultra-nationalist who blames his country's problems on the Jews", who is "obviously an analogue of a historical figure" — results in an emphasis on the "artificial, game-like nature of [Reed's] scenario", ultimately detracting from readers' suspension of disbelief.
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3D model of a small retrosnub icosicosidodecahedron In geometry, the small retrosnub icosicosidodecahedron (also known as a retrosnub disicosidodecahedron, small inverted retrosnub icosicosidodecahedron, or retroholosnub icosahedron) is a nonconvex uniform polyhedron, indexed as U72. It has 112 faces (100 triangles and 12 pentagrams), 180 edges, and 60 vertices. It is given a Schläfli symbol ß{,5}. The 40 non-snub triangular faces form 20 coplanar pairs, forming star hexagons that are not quite regular.
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In mathematics, a stuck unknot is a closed polygonal chain that is topologically equal to the unknot but cannot be deformed to a simple polygon by rigid motions of the segments.G. Aloupis, G. Ewald, and G. T. Toussaint, "More classes of stuck unknotted hexagons," Contributions to Algebra and Geometry, Vol. 45, No. 2, 2004, pp. 429–434.G. T. Toussaint, "A new class of stuck unknots in Pol-6," Contributions to Algebra and Geometry, Vol.
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The Kotva department store was created between 1970 and 1975, designed by Czech architect couple Věra Machoninová and Vladimir Machonin. It was built by the Swedish construction company SIAB, which was at that time very unusual. The floor plan consists of multiple intertwined hexagons. Kotva has five stories above ground, a total of ten interconnected escalators (two shafts of five escalators) and about the same number underground, serving as a garage and supermarket.
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In two dimensions the analogous figure to a parallelohedron is a parallelogon, a polygon that can tile the plane edge-to-edge by translation. These are parallelograms and hexagons with opposite sides parallel and of equal length. In higher dimensions a parallelohedron is called a parallelotope. There are 52 different four-dimensional parallelotopes, first enumerated by Boris Delaunay (with one missing parallelotope, later discovered by Mikhail Shtogrin), and 103769 types in five dimensions.
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An example implementation of the image preprocessing steps in a traffic-sign detection algorithm There are diverse algorithms for traffic-sign recognition. Common ones are those based on the shape of the sign board. Typical sign board shapes like hexagons, circles, and rectangles define different types of signs, which can be used for classification. Other major algorithms for character recognition includes Haar-like features, Freeman Chain code, AdaBoost detection and deep learning neural networks methods.
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The pulpit and the mosaic floor The inlaid marble mosaic floor is one of the most ornate of its kind in Italy, covering the whole floor of the cathedral. This undertaking went on from the 14th to the 16th centuries, and about forty artists made their contribution. The floor consists of 56 panels in different sizes. Most have a rectangular shape, but the later ones in the transept are hexagons or rhombuses.
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The QIMR Berghofer logo is composed of three superimposed hexagons, which represent interlocking benzene rings. Benzene rings are a molecular structure of carbon, the basis for all life on earth. QIMR Berghofer came together with Children’s Health Queensland, Mater Health Services, Metro North Hospital and Health Service, Metro South Health, Queensland University of Technology, The University of Queensland and the Translational Research Institute to form Brisbane Diamantina Health Partners, Queensland's first academic health science system.
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Piers of clustered narrow round columns support arches and an entablature. Windows on the upper levels are set in segmented-arch openings, with bracketed lintels and eared hoods that are joined by a stone stringcourse. The windows in the center of the Middle Street facade are more ornately decorated, and the building has a cornice with paired brackets, and bands of freestone hexagons and quatrefoils between. The Church Street facade has similar but simpler styling.
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Two possible explanations exist as to why honeycomb is composed of hexagons, rather than any other shape. First, the hexagonal tiling creates a partition with equal-sized cells, while minimizing the total perimeter of the cells. Known in geometry as the honeycomb conjecture, this was given by Jan Brożek and proved much later by Thomas Hales. Thus, a hexagonal structure uses the least material to create a lattice of cells within a given volume.
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The pores easily take up six atoms per unit cell, as a hexagonal arrangement in the pores, with each neon atom close to a nickel atom. A seventh neon atom can be forced under pressure at the centre of the neon hexagons. Neon is pushed into crystals of ammonium iron formate (NH4Fe(HCOO)3) and ammonium nickel formate (NH4Ni(HCOO)3) at 1.5 GPa to yield Ne•NH4Fe(HCOO)3 and Ne•NH4Ni(HCOO)3.
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Double hexagons and octagons are the most common variations. Since the introduction of #H#V mixed- order schemes by Travis (2009),Travis, Chris, A new mixed-order scheme for Ambisonic signals , Ambisonics Symposium, Graz 2009 stacked rings can be operated at their full horizontal resolution even for elevated sources. #H#V decoding matrices for common layouts are available from Adriaensen (2012). Triple rings are rare, but have been used to good effect.
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The first iterations supported 64 players per server instance in one region, eventually leading to 120 player support. World Conquest, the primary game mode in Foxhole, was first released in March 2018. On release, the game mode featured 9 interlocking regions on global conflict. As of Update 26, released on 19 June 2019, the map was completely redesigned so that all regions are hexagons of equal size and increased the number of regions to 23.
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The illustration shows Adaptiv mimicking a four wheel drive car, using part of the panel, while the rest of the panel is cryptic, imitating the natural background. The technology is said to reduce the range at which a vehicle would be detected to less than 500 metres. The panels forming Adaptiv's pixels are hexagons approximately 5.5 inches (14 cm) wide. They are robust, contributing to the armour of the vehicle that carries them.
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The shape of the pillars in this house also varies, there are rectangles, hexagons, heptagon, octagon and triangles. Each type of pole contained in this traditional house has meaning believed by the people of Riau. A rectangular pole can be interpreted as four corners of the wind, just like an octagon, and the hexagon symbolizes the number of pillars of Islam. Rumah Salaso Jatuh Kembar was declared an icon and symbol of the province of Riau.
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The shapes and angles of floor plans and design motifs were based on the hexagon. The initial layout of the Humanities building envisioned two or three teachers and their respective students sharing a single open plan hexagonal room, but this quickly proved too distracting. Portable office dividers were placed in a line to define classroom boundaries, but noise was still a problem. After two years of such conditions, walls were erected to close off the large, open hexagons.
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There are, up to isomorphism, precisely two generalized hexagons of order (2,2) as proved by Cohen and Tits. They are the split Cayley hexagon H(2) and its point-line dual. Clearly both of them have the same incidence graph, which is in fact isomorphic to the Tutte 12-cage. The Balaban 11-cage can be constructed by excision from the Tutte 12-cage by removing a small subtree and suppressing the resulting vertices of degree two.
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The game is about penguins trying to catch fish on the Antarctic. The game board is made of connected hexagons, each with one, two or three fish. After the game board has been built, each player chooses a colour and is assigned a number of penguins: four for a two- player game, three for a three-player game, or two for a four-player game. These penguins are then placed onto any vacant hexagon containing one fish.
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The HEX battle system is composed of seven hexagons on the battle field, with random beginning placement for all characters and enemies. What makes the HEX battle system so unique is that it is area based instead of character based. This means that any attacks or spells given to certain hexagon, or HEX, will affect all characters on that HEX. Multiple allies or enemies can occupy a single HEX, but enemies and allies can't occupy the same HEX.
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Davi & Charles Brunel House, Wisconsin. 2005. Mostly geometric patterns are used to make this work. There are two main styles: moyōzashi, in which patterns are created with long lines of running stitches; and hitomezashi, where the pattern emerges from the alignment of single stitches made on a grid. Common motifs used in sashiko are waves, mountains, bamboo, bishamon, key fret, double cypress fence, arrow feathers, seven treasures, pampas grass, overlapping diamonds, linked diamonds, lightning, linked hexagons and persimmon flower.
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Triangles do not work, exhibiting large "holes" between the speakers. Regular Hexagons perform better than Squares especially to the sides. For the simplest (two dimensional) case (no height information), and spacing the loudspeakers equally in a circle, we derive the loudspeaker signals from the B-format W, X and Y channels: :P_n = W + X \cos\theta_n + Y \sin\theta_n where \theta_n is the direction of the speaker under consideration. The most useful of these is the Square 4.0 decoder.
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All kites tile the plane by repeated inversion around the midpoints of their edges, as do more generally all quadrilaterals. A kite with angles π/3, π/2, 2π/3, π/2 can also tile the plane by repeated reflection across its edges; the resulting tessellation, the deltoidal trihexagonal tiling, superposes a tessellation of the plane by regular hexagons and isosceles triangles.See . The deltoidal icositetrahedron, deltoidal hexecontahedron, and trapezohedron are polyhedra with congruent kite-shaped facets.
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The rotunda is in circumference and rises to a cupola which in high and long. The rotunda also contains ten stained-glass windows and clerestory.John F. Werner, The New York County Courthouse: A Brief Architectural/Design History (March 12, 2008). Material printed in conjunction with the talk "Circles and Hexagons upon a Square: Urbanism, Architecture and Civic Identity at 60 Centre Street" (March 12, 2008) by Jon Ritter, Assistant Professor in the Department of History at New York University.
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Toyoma Education Museum exhibits the history of education in Japan since the Meiji period. It is housed in the of 1888 in the city of Tome, Miyagi Prefecture. The U-shaped two-storey building around a courtyard, lined with balconies and with half-hexagons at the end of each wing, was designed by Kisaburo Yamazoe. It is representative of the western-inspired architecture of the Meiji period and in 1981 was designated an Important Cultural Property.
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A view of Lake Tillery from the Fall Mountain Trail Laurel Trail: , blazed with red hexagons. This short loop trail goes around the Morrow Mountain camping area in deep forest and tall undergrowth. The trail starts at the far end of the camp office parking lot and loops before returning to the start. Turning right at the start of the loop will take you through a deep thicket of undergrowth before finally emerging in deep woods.
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Mechlin lace is also more expensive than Valenciennes lace, as it takes more time to make because of the different réseau. Sometimes Mechlin is grounded with an ornamental réseau, instead of the usual hexagons. In the regular hexagonal réseau, the two sides parallel to the long axis of the lace are plaited three times, and the other four sides crossed. The same threads pass across the whole width, and thus form both the ground and the pattern.
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In connection with the inscribed square problem, observed that the Reuleaux triangle provides an example of a constant-width shape in which no regular polygon with more than four sides can be inscribed, except the regular hexagon, and he described a small modification to this shape that preserves its constant width but also prevents regular hexagons from being inscribed in it. He generalized this result to three dimensions using a cylinder with the same shape as its cross section..
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Scoring occurs from each of the two symbols on the tile. Counting outwards in a straight line from each of the five available faces of the two hexagons (the symbols on the tile itself are not counted), one point is scored in that tile's color for each identical symbol in an unbroken line. It is therefore possible to score points on two colors by placing a single tile. Each player's score is public knowledge at all times.
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Einfach Genial Knobelspass (Simply Ingenious Puzzles), also from Kosmos, uses cardboard versions of the tiles from the original game. The player has one of each of the 21 different tile combinations and for each puzzle must place these in the correct positions on a pre-printed sheet to match the coloured symbols. Einfach Genial Junior is a simpler version of the game. It uses similar techniques of matching coloured symbols but utilises a square board instead of hexagons.
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Honeycomb section containing transition from worker to drone (larger) cells – here bees make irregular and five-cornered cells (marked with red dots). Western honeybees and honeycomb In 1965, László Fejes Tóth discovered the trihedral pyramidal shape (which is composed of three rhombi) used by the honeybee is not the theoretically optimal three- dimensional geometry. A cell end composed of two hexagons and two smaller rhombuses would actually be .035% (or about one part per 2850) more efficient.
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Kikko armor was made for every class of samurai or soldier, high or low. George Cameron StoneGeorge Cameron Stones, "A Glossary of the Construction, Decoration and Use of Arms and Armor: in All Countries and in All Times" p.150 referred to kikko as "brigandine" when he said "in Japan brigandines were often used". He further described this "brigandine" as "small hexagons", "the plates [being] of steel or hard leather", and that "occasionally they covered the whole body".
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The most common variety of n-flake is two-dimensional (in terms of its topological dimension) and is formed of polygons. The four most common special cases are formed with triangles, squares, pentagons, and hexagons, but it can be extended to any polygon. Its boundary is the von Koch curve of varying types - depending on the n-gon - and infinitely many Koch curves are contained within. The fractals occupy zero area yet have an infinite perimeter.
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3D model of a great truncated cuboctahedron In geometry, the great truncated cuboctahedron (or quasitruncated cuboctahedron or stellatruncated cuboctahedron) is a nonconvex uniform polyhedron, indexed as U20. It has 26 faces (12 squares, 8 hexagons and 6 octagrams), 72 edges, and 48 vertices. It is represented by the Schläfli symbol tr{4/3,3}, and Coxeter-Dynkin diagram, . It is sometimes called the quasitruncated cuboctahedron because it is related to the truncated cuboctahedron, , except that the octagonal faces are replaced by {8/3} octagrams.
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Both of these observations are used to estimate the intensity of tropical cyclones via Dvorak analysis. Eyewalls are typically circular; however, distinctly polygonal shapes ranging from triangles to hexagons occasionally occur. While typical mature storms have eyes that are a few dozen miles across, rapidly intensifying storms can develop an extremely small, clear, and circular eye, sometimes referred to as a pinhole eye. Storms with pinhole eyes are prone to large fluctuations in intensity, and provide difficulties and frustrations for forecasters.
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These benefits were expected to overcome the added complication of a using chemically reactive coolant. The reactor was initially fueled with 3.6% enriched uranium-10 molybdenum alloy with stainless steel cladding. The graphite moderator was clad in stainless steel hexagons with each corner scalloped to make room for the process tubes which contained the fuel clusters and control rods. Three sodium heat-transfer loops (each with a radioactive primary loop and a non- radioactive secondary) moved heat to three steam generators.
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Within this latter device, the Preston coat of arms rests above a supporting group of eagles, foliage and scrolls, terminating at either side with cherub's heads in profile. A likely inspiration for this design is the Livre d'Architecture by French architect Jean Barbet. Robert Pricke used Barbet's pattern in his 1674 work The Architect's Store-House. In his Book of Sundry Draughts (1615), Walter Gedde included a pattern repeated on the floor of this room in stone flags, the squares and hexagons intersecting.
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If the data being manipulated is the important aspect of the program, why isn't the data the "first class citizen" of the programming language? Working on that basis, a number of new programming systems evolved, including object- oriented programming and dataflow programming. Prograph took these concept further, introducing a combination of object-oriented methodologies and a completely visual environment for programming. Objects are represented by hexagons with two sides, one containing the data fields, the other the methods that operate on them.
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Snyder equal-area projection is used in the ISEA (Icosahedral Snyder Equal Area) discrete global grids. The first projection studies was conducted by John P. Snyder in the 1990s. Snyder, J. P. (1992), “An Equal-Area Map Projection for Polyhedral Globes”, Cartographica, 29(1), 10-21. urn:doi:10.3138/27H7-8K88-4882-1752. It is a modified Lambert azimuthal equal-area projection, most adequate to the polyhedral globe, a truncated icosahedron with 32 same-area faces (20 hexagons and 12 pentagons).
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Holdridge life zone classification scheme. Although conceived as three-dimensional by its originator, it is usually shown as a two-dimensional array of hexagons in a triangular frame. Holdridge classified climates based on the biological effects of temperature and rainfall on vegetation under the assumption that these two abiotic factors are the largest determinants of the types of vegetation found in a habitat. Holdridge uses the four axes to define 30 so- called "humidity provinces", which are clearly visible in his diagram.
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In 1855, the U.S. inventor Charles Goodyear – who had patented vulcanised rubber – exhibited a spherical football, with an exterior of vulcanised rubber panels, at the Paris Exhibition Universelle. The ball was to prove popular in early forms of football in the U.S.soccerballworld.com, (no date) "Charles Goodyear's Soccer Ball" Downloaded 30/11/06. The iconic ball with a regular pattern of hexagons and pentagons (see truncated icosahedron) did not become popular until the 1960s, and was first used in the World Cup in 1970.
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Two hexagons and two triangles alternate around each vertex, and its edges form an infinite arrangement of lines. Its dual is the rhombille tiling. This pattern, and its place in the classification of uniform tilings, was already known to Johannes Kepler in his 1619 book Harmonices Mundi.. The pattern has long been used in Japanese basketry, where it is called kagome. The Japanese term for this pattern has been taken up in physics, where it is called a Kagome lattice.
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Related to polyominoes are polyiamonds, formed from equilateral triangles; polyhexes, formed from regular hexagons; and other plane polyforms. Polyominoes have been generalized to higher dimensions by joining cubes to form polycubes, or hypercubes to form polyhypercubes. In statistical physics, the study of polyominoes and their higher-dimensional analogs (which are often referred to as lattice animals in this literature) is applied to problems in physics and chemistry. Polyominoes have been used as models of branched polymers and of percolation clusters.
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A Fokker D.VII shows a four-color Lozenge-Tarnung (lozenge camouflage) During the First World War, the Germans developed Lozenge-Tarnung (lozenge camouflage). This camouflage was made up of colored polygons of four or five colors. The repeating patterns often used irregular four-, five- and six-sided polygons, but some contained regular rhombi or hexagons. Because painting such a pattern was very time consuming, and the paint added considerably to the weight of the aircraft, the pattern was printed on fabric.
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Comment by Parts on Polymath Thread 16, August 3, 2019 The page of the Polymath project, , contains further research, media citations and verification data. The upper bound of seven on the chromatic number follows from the existence of a tessellation of the plane by regular hexagons, with diameter slightly less than one, that can be assigned seven colors in a repeating pattern to form a 7-coloring of the plane. According to , this upper bound was first observed by John R. Isbell.
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Mosque of Ibn Tulun: window with girih- style 10-point stars (at rear), with floral roundels in hexagons forming a frieze at front Jali are pierced stone screens with regularly repeating patterns. They are characteristic of Indo-Islamic architecture, for example in the Mughal dynasty buildings at Fatehpur Sikri and the Taj Mahal. The geometric designs combine polygons such as octagons and pentagons with other shapes such as 5- and 8-pointed stars. The patterns emphasized symmetries and suggested infinity by repetition.
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3D model of a truncated icosahedron In geometry, the truncated icosahedron is an Archimedean solid, one of 13 convex isogonal nonprismatic solids whose 32 faces are two or more types of regular polygons. It has 12 regular pentagonal faces, 20 regular hexagonal faces, 60 vertices and 90 edges. It is the Goldberg polyhedron GPV(1,1) or {5+,3}1,1, containing pentagonal and hexagonal faces. This geometry is associated with footballs (soccer balls) typically patterned with white hexagons and black pentagons.
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Fisher's interests have included microphotography, using both a scanning electron microscope (SEM), and an optical microscope; also aerial photography, photographic research in Morocco, and mixed media painting including geometric patterns and collage. While studying at Otis Art Institute, Fisher began to focus on geometric patterns and sacred geometry (geometry found in sacred art and architecture). Her fascination with geometric patterns has led her to explore them throughout her career. Through her work with SEMs and bees, she began to focus on hexagons.
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The waves can take the form of stripes, close-packed hexagons, or even squares or quasiperiodic patterns. Faraday waves are commonly observed as fine stripes on the surface of wine in a wine glass that is ringing like a bell. Faraday waves also explain the 'fountain' phenomenon on a singing bowl. The Faraday wave and its wavelength is analogous to the de Broglie wave with the de Broglie wavelength in De Broglie–Bohm theory in the field of quantum mechanics .
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UPC-A barcode symbol A barcode or bar code is a method of representing data in a visual, machine-readable form. Initially, barcodes represented data by varying the widths and spacings of parallel lines. These barcodes, now commonly referred to as linear or one-dimensional (1D), can be scanned by special optical scanners, called barcode readers. Later, two-dimensional (2D) variants were developed, using rectangles, dots, hexagons and other geometric patterns, called matrix codes or 2D barcodes, although they do not use bars as such.
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His headstrong nature, combined with the talents of his fellow crew, enable Dai-Guard to be victorious against multiple Heterodyne attacks causing the military to want it back. Heterodyne are mysterious entities formed from dimensional quakes all around Japan and are attracted to electromagnetic hot-spots. Crystalline hexagons called Fractal Knots act as their nucleus and they form bodies using the matter around them. Although Fractal Knots replicate themselves indefinitely, if the original is destroyed it will immediately reduce the rest of the body into ethanol.
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Each of these radially equilateral polytopes also occurs as cells of a characteristic space-filling tessellation: the tiling of regular hexagons, the rectified cubic honeycomb (of alternating cuboctahedra and octahedra), the 24-cell honeycomb and the tesseractic honeycomb, respectively. Each tessellation has a dual tessellation; the cell centers in a tessellation are cell vertices in its dual tessellation. The densest known regular sphere-packing in two, three and four dimensions uses the cell centers of one of these tessellations as sphere centers. A cuboctahedron has octahedral symmetry.
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The light chains bind primarily to the proximal leg portion of the heavy chain with some interaction near the trimerization domain. The β-propeller at the 'foot' of clathrin contains multiple binding sites for interaction with other proteins. When triskelia assemble together in solution, they can interact with enough flexibility to form 6-sided rings (hexagons) that yield a flat lattice, or 5-sided rings (pentagons) that are necessary for curved lattice formation. When many triskelions connect, they can form a basket-like structure.
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17 Cranston Street stands on top of a low ridge southeast of the Hyde Square junction of Centre and Perkins Streets in Jamaica Plain. The main structure consists of three four-sided bays resembling truncated hexagons, which have been joined together in a Y shape around a central hexagon. Windows consist of paired casements, each set at one of the angled corners with a triangular colored transom, giving the pair the appearance of a peaked transom. Each window pair is framed by shouldered Italianate moulding.
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In strategy mode, the overview map is made of a series of interlocking hexagons (called Hexes). On most maps, both sides have a base occupying a single Hex that can be used to buy or sell units. The player's aim is to destroy all of their opponent's units and their base. Strategy mode is turn-based; the player is allowed to make up to three moves before control switches to their opponent, who then makes three moves before said player regains control and so on.
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Prior to starting, the game map has to be assembled. The board consists of separate map hexagons representing coastal, highland and plains terrain, which are to be placed together to form a unique playing field. There are specific rules as to how the map tiles can be placed in order to maintain a sense of realism about the geography. For example, a river should continue until it terminates in a coastal, lake or swamp tile, rather than terminating abruptly by a blocking mountain or plains tile.
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Three Rivers Trail: Officially considered the nature trail of the park, this trail, blazed with blue hexagons, has seen better days. Many of the piers that once dotted the Tillery shoreline have fallen in, but the trail is still commonly hiked. The trail, starting in the Tillery/Boathouse parking lot, goes through marshes and woods, connecting all of the park's ecosystems along one short trail. After passing through marshland and coastline, the trail ascends a small hill, where hikers can find deep woods and wildflowers.
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An Afghan blanket of granny squares during piecework assembly A scarf made from hexagonal granny squares in mixed color cotton yarn bordered with ecru According to Edie Eckman in The Crochet Answer Book, Any granny square begins with a small loop of chain stitches. Basic granny squares alternate sets of double stitches and chain stitches. Variant patterns use different stitch types or produce other geometric shapes such as hexagons. In order to achieve a distinct angle at the corners the designer uses extra chain stitches.
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The match ball for this game was the Adidas Fevernova, a ball specifically made for the World Cup. The ball's design was different from the normal "Tango" type of three-pointed shapes connecting each hexagon, instead introducing a different, triangle-like shape on four hexagons. This look and color usage was entirely based on Asian culture. It also featured a refined syntactic foam layer, to give the ball superior performance characteristics, and a three-layer knitted chassis, allowing for a more precise and predictable flight path.
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The Battle of the Hydaspes. General Porus currently has the initiative; his command radius is indicated by the lighter-colored hexagons across the top of the battlefield. The Great Battles of Alexander is a computer wargame, which recreates the historical military exploits of Alexander the Great via turn-based gameplay. The game takes place on a hex map, and simulates combat at the tactical level; the player navigates an army of predetermined units on discrete battlefields, in a manner that one commentator compared to chess.
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The building is formed by hexagons, with a hyperbolic parabolic roof, creating a distinctive skyline and interior. Morecambe once boasted two fairgrounds: a small one to the north of the railway station, which closed down in the 1980s, and a larger one to the south of the station, which ultimately became Frontierland and closed in 1999. The last remaining landmark on the site was the Polo Tower, left standing only because of the contract for the phone mast on top. This was demolished mid 2017.
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Its dihedral angle is approximately 138.19°. Thus, just as hexagons have angles not less than 120° and cannot be used as the faces of a convex regular polyhedron because such a construction would not meet the requirement that at least three faces meet at a vertex and leave a positive defect for folding in three dimensions, icosahedra cannot be used as the cells of a convex regular polychoron because, similarly, at least three cells must meet at an edge and leave a positive defect for folding in four dimensions (in general for a convex polytope in n dimensions, at least three facets must meet at a peak and leave a positive defect for folding in n-space). However, when combined with suitable cells having smaller dihedral angles, icosahedra can be used as cells in semi-regular polychora (for example the snub 24-cell), just as hexagons can be used as faces in semi-regular polyhedra (for example the truncated icosahedron). Finally, non-convex polytopes do not carry the same strict requirements as convex polytopes, and icosahedra are indeed the cells of the icosahedral 120-cell, one of the ten non-convex regular polychora.
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The initial site plan foresaw the subsequent addition of two buildings to create a grid of three connected hexagons, however, after a change in management, it was indicated that further construction in the original style would not occur. Instead a conventional office block was built adjacent to it known as "Whitehouse Station West". In the center of the building there is a park with a small lawned sitting area containing a statue given by Merck Germany. Prior to moving to this location, the Merck & Co. headquarters was located in Rahway, New Jersey.
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Some interesting fold-out nets of the cube, octahedron, dodecahedron and icosahedron are available here. Numerous children's toys, generally aimed at the teen or pre-teen age bracket, allow experimentation with regular polygons and polyhedra. For example, klikko provides sets of plastic triangles, squares, pentagons and hexagons that can be joined edge-to-edge in a large number of different ways. A child playing with such a toy could re-discover the Platonic solids (or the Archimedean solids), especially if given a little guidance from a knowledgeable adult.
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Galileo attempts to clarify the matter by considering hexagons and then extending to rolling 100 000-gons, or n-gons, where he shows that a finite number of finite slips occur on the inner shape. Eventually, he concludes "the line traversed by the larger circle consists then of an infinite number of points which completely fill it; while that which is traced by the smaller circle consists of an infinite number of points which leave empty spaces and only partly fill the line," which would not be considered satisfactory now.
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Even if all 20 hexagons were filled (which did occur at least twice, once in the very first series, and once in the first Sky version) there would always be a winner. The game began with a toss-up question to play for control of the board, starting with a letter that was chosen at random. The teams or players could buzz-in during the middle of reading of a question. If a player or team got the correct answer, they gained control of that hexagon and were given the chance to choose another one.
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The official logo of the 2019 AFC Asian Cup was unveiled on 23 January 2017 in Abu Dhabi during the drawing ceremony for the third round of the 2019 AFC Asian Cup qualification. The colors used in the logo were derived from the flag of the UAE. The seven hexagons formed by colored ribbons represents the seven emirates of the host country. The interlacing hexagon pattern of the logo was inspired from Islamic art, as well as the old Emirati tradition of using palm leaves, locally known as saf, in weaving.
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Resch and his team tiled the egg using a total of 1108 congruent equilateral triangles, 524 concave hexagons (3-pointed stars), 3,512 visible facets, 6,978 nuts and bolts and 177 internal struts. The tiles range in thickness from to and are jointed at angles ranging from 1° at the center to 7° at the tips. These are held together by an internal framework of radiating spokes, which connect the egg's "shell." The pysanka leans at a 30° relative to the base, and turns with the wind similar to the motions of a weather vane.
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Irregular dodecahedron The Weaire–Phelan structure differs from Kelvin's in that it uses two kinds of cells, although they have equal volume. From a topological and symmetrical point of view, one is a pyritohedron, an irregular dodecahedron with pentagonal faces, possessing tetrahedral symmetry (Th). Tetrakaidecahedron The second is a form of truncated hexagonal trapezohedron, a species of tetrakaidecahedron with two hexagonal and twelve pentagonal faces, in this case only possessing two mirror planes and a rotoreflection symmetry. Like the hexagons in the Kelvin structure, the pentagons in both types of cells are slightly curved.
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A round caisson in the imperial garden at the Forbidden City The caisson (), also referred to as a caisson ceiling, or spider web ceiling, in East Asian architecture is an architectural feature typically found in the ceiling of temples and palaces, usually at the centre and directly above the main throne, seat, or religious figure. The caisson is generally a sunken panel set into the otherwise largely flat ceiling. It is often layered and richly decorated. Common shapes include squares, octagons, hexagons, circles, and a combination of these.
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The geometric proof of the classification in the previous paragraph is important to understand the structure of hyperbolic pants. It proceeds as follows: given an hyperbolic pair of pants with totally geodesic boundary the three geodesic arcs joining the cuffs pairwise and which are perpendicular to them at their ends are uniquely determined, and are called the seams of the pants. Cutting the pants along the seams one gets two right-angled hyperbolic hexagons which have three alternate sides of matching lengths. The following lemma can be proven with elementary hyperbolic geometry.
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Inspired by the three-dimensional The Legend of Zelda games with some role-playing game elements, the player assumes the role of Goemon, who is set once again to save Japan. Goemon is able to use a large variety of weapons (including his trademark pipe), as well as equip sub-weapons, items and magic, which can be assigned in 4 hexagons for quick use. Another twist is the addition of a white tiger known as Kotora, whom Goemon can use to attack enemies when he locks on them.
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The pigment cells line the outside of each ommatidium. Each pigment cell is situated at the apex of the hexagons and thus lines the outside of three ommatidia. Light entering at an angle passes through the thin cross-section of the photoreceptor cell, with only a tiny chance of exciting it, and is absorbed by the pigment cell, before it can enter a neighboring ommatidium. In many species, in low-light situations, the pigment is withdrawn, so that light entering the eye might be detected by any of several ommatidia.
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The only spike of Influenza C virus, the hemagglutinin‐esterase‐fusion glycoprotein (HEF) combines receptor binding, receptor hydrolysis and membrane fusion activities. Like other hemagglutinating glycoproteins of influenza viruses HEF is S‐acylated, but only with stearic acid at a single cysteine located at the cytosol‐facing end of the transmembrane region. This HE protein however, has spikes in its structural organization as well. HEF trimers on the surfaces of both spherical and filamentous particles are arranged in a reticular structure that has been described to consist mainly of hexagons.
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Conflict of Heroes (CoH) is a tactical-level board wargame series that simulates firefights at the platoon or company level. Several games and expansions have been released in the series including, Price of Honour set in Poland in 1939, Awakening the Bear!, set in the World War II Eastern Front between the years 1941 and 1942, Storms of Steel, set in Kursk in 1943 and Guadalcanal, set on Guadalcanal in 1942. The game is played on one or more interchangeable map boards which are divided into hexagons for movement and firing regulation.
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The discoverers of the allotrope named the newfound molecule after Buckminster Fuller, who designed many geodesic dome structures that look similar to C60 and who had died the previous year in 1983 before discovery in 1984. This is slightly misleading, however, as Fuller's geodesic domes are constructed only by further dividing hexagons or pentagons into triangles, which are then deformed by moving vertices radially outward to fit the surface of a sphere. Geometrically speaking, buckminsterfullerene is a naturally-occurring example of a Goldberg polyhedron. A common, shortened name for buckminsterfullerene is "buckyballs".
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Following an international contest for the city's design, a blueprint by American architects Walter Burley Griffin and Marion Mahony Griffin was selected and construction commenced in 1913. The Griffins' plan featured geometric motifs such as circles, hexagons and triangles, and was centred on axes aligned with significant topographical landmarks in the Australian Capital Territory. The city's design was influenced by the garden city movement and incorporates significant areas of natural vegetation. As the seat of the government of Australia, Canberra is home to many important institutions of the federal government, national monuments and museums.
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Other two dimensional shapes than squares can be considered. The general case is to consider a design with N parts to be magic if the N parts are labeled with the numbers 1 through N and a number of identical sub-designs give the same sum. Examples include magic circles, magic rectangles, magic trianglesMagic Designs, Robert B. Ely III, Journal of Recreational Mathematics volume 1 number 1, January 1968 magic stars, magic hexagons, magic diamonds. Going up in dimension results in magic spheres, magic cylinders, magic cubes, magic parallelepiped, magic solids, and other magic hypercubes.
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Advanced Squad Leader (ASL) is a tactical-level board wargame, originally marketed by Avalon Hill Games, that simulates actions of squad sized units in World War II. It is a detailed game system for two or more players (with solitary play also possible). Components include the ASL Rulebook and various games called modules. ASL modules provide the standard equipment for playing ASL, including geomorphic mapboards and counters. The mapboards are divided into hexagons to regulate fire and movement, and depict generic terrain that can represent different historical locations.
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Tiles found at Takht-e Soleyman are great artistic marks that demonstrate the interaction with and influence from China during the fourteenth century. There were six types of tiles: unglazed, partly glazed, monochrome glazed, luster-painting, Lajvardina (cobalt blue and white), and inglazed Lajvardina. The exterior tiles, including unglazed, partly glazed and monochrome glazed, are shaped as hexagons and composed with reddish clay, with turquoise or blue coloring. The design is inspired by Mongol and Chinese ceramics, mainly from ceramics including dragon or phoenix motifs, and an interwoven line design.
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In the Euclidean plane there are 3 regular forms equilateral triangle, squares, and regular hexagons; and 8 semiregular forms; and 4-demiregular forms which can tile the plane with other planigons. All angles of a planigon are whole divisors of 360°. Tilings are made by edge-to-edge connections by perpendicular bisectors of the edges of the original uniform lattice, or centroids along common edges (they coincide). Tilings made from planigons can be seen as dual tilings to the regular, semiregular, and demiregular tilings of the plane by regular polygons.
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The "banner" rises 112 vertical feet in front of the church and houses the 5 bells which sound the hours and call the monastic and university communities to prayer. The north facade of the building is the largest wall of stained glass in the world and contains 430 colorful hexagons of abstract design. Construction of the church began on May 19, 1958, and lasted until August 24, 1961. The church was consecrated in the fall of 1961 and serves to this day as the principal liturgical space of both the monastic community and the university.
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Its form is a series of hexagons radiating from a central chimney or service core without any true right angles, with many different wings off it for a nursery, terrace, guest room and carport. The cypress and brick house came to be known as Snowflake because of the hexagonal patterns created by the diamond grid design. This was the first use of Wright's modular diamond structure in Michigan, a technique he used elsewhere when incorporating a house into a hillside. A massive brick retaining wall supports a dramatic terrace.
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Example of frequency reuse factor or pattern 1/4 In a cellular radio system, a land area to be supplied with radio service is divided into cells in a pattern dependent on terrain and reception characteristics. These cell patterns roughly take the form of regular shapes, such as hexagons, squares, or circles although hexagonal cells are conventional. Each of these cells is assigned with multiple frequencies (f1 – f6) which have corresponding radio base stations. The group of frequencies can be reused in other cells, provided that the same frequencies are not reused in adjacent cells, which would cause co- channel interference.
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This technique also allows a larger number of slices to be extracted from the same amount of clay. In glass work, the type of the material dictates that these be round, but with polymer clay the shapes can be more varied, although round and square canes are the most common because they are easiest to extend. Cylinders can be rolled out to a longer length very easily, while cubic forms can be squeezed on their four side surfaces. More complex shapes such as hexagons can be worked with, but it is difficult to extend complex shapes without distortion.
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The nanoparticles formed in this method have a size range between 5 and 15 nm and consist of silver hydrosol. The reduction of the silver nanoparticles is thought to come from an enzymatic process and silver nanoparticles produced are extremely stable due to interactions with proteins that are excreted by the fungi. Bacterium found in silver mines, Pseudomonas stutzeri AG259, were able to construct silver particles in the shapes of triangles and hexagons. The size of these nanoparticles had a large range in size and some of them reached sizes larger than the usual nanoscale with a size of 200 nm.
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If the cuboctahedron is cut in the plane of one of these hexagons, each half is a triangular cupola, one of the Johnson solids; the cuboctahedron itself thus can also be called a triangular gyrobicupola, the simplest of a series (other than the gyrobifastigium or "digonal gyrobicupola"). If the halves are put back together with a twist, so that triangles meet triangles and squares meet squares, the result is another Johnson solid, the triangular orthobicupola, also called an anticuboctahedron. Both triangular bicupolae are important in sphere packing. The distance from the solid's center to its vertices is equal to its edge length.
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Under some conditions, carbon crystallizes as lonsdaleite, a hexagonal crystal lattice with all atoms covalently bonded and properties similar to those of diamond. Fullerenes are a synthetic crystalline formation with a graphite-like structure, but in place of flat hexagonal cells only, some of the cells of which fullerenes are formed may be pentagons, nonplanar hexagons, or even heptagons of carbon atoms. The sheets are thus warped into spheres, ellipses, or cylinders. The properties of fullerenes (split into buckyballs, buckytubes, and nanobuds) have not yet been fully analyzed and represent an intense area of research in nanomaterials.
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Sucking disc of Sicyases sanguineus (viewed from below with mouth at the top) Clingfish are named for their ability to firmly attach themselves to various surfaces, even in strong water currents or when battered by waves. This ability is aided by their sucking disc, which is located on the underside at the chest and is formed primarily by modified pelvic fins and adjacent tissue. In some species it is divided in two, resulting in a larger front and a smaller rear sucking disc. The sucking disc is covered in tiny hexagons and each of these consists of many microscopic hair-like structures (setae).
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Sage has been interested by textiles for much of her life, she remembers "early childhood days spent round a table with my sister making cards, being taught to crochet and sewing patchwork hexagons."Kathleen Laurel Sage: About Me Following this initial fascination she began to see textiles as a career path and studied in different areas of embroidery and design. Sage spent 9 years studying to gain City and Guilds part 1 & 2 in Patchwork and Quilting and part 1 & 2 in Embroidery. Then in 1998 Sage embarked on an OCN Diploma in Textiles at Treshem Institute in Kettering.
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However, a 1999 renovation subsequently removed the IND style and replaced it with the BMT quilt-like tile pattern that exists on all other subway stations on the BMT Canarsie Line. The current tile color scheme is white with red stripes and mosaics held in beige and tan, with a pattern of red, yellow, green and off-white in the center. To signify the station's location, there are small "8" decorations set in teal-green hexagons, as found in other stations on the line. On April 18, 2004, an L train ran into the bumper block after the operator suffered a seizure.
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KristalLabs further developed K2 in cooperation with the American music technology company, PreSonus, before becoming part of PreSonus in 2009. Following this acquisition, the final result of the K2 development was re-branded and released as the first version of the PreSonus DAW, Studio One, for macOS and Windows. The former KristalLabs logo (representing a series of hexagons, like the one from the original KRISTAL Audio Engine logo, tessellated together) was used as the basis for the logo of Studio One. Since this time, all versions of Studio One have been developed and released by PreSonus.
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At the time it was built, the dome was the highest in the Ottoman Empire when measured from sea level, but lower from the floor of the building and smaller in diameter than that of the nearby Hagia Sophia. Another Classical domed mosque type is, like the Byzantine church of Sergius and Bacchus, the domed polygon within a square. Octagons and hexagons were common, such as those of Üç Şerefeli Mosque (1437–1447) and Selimiye Mosque in Edirne. The Selimiye Mosque was the first structure built by the Ottomans that had a larger dome than that of the Hagia Sophia.
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Its exterior boundary is the Koch snowflake, and the full boundary contains an infinite number of Koch snowflakes. The Hausdorff dimension of the hexaflake is equal to ln(7)/ln(3), approximately 1.7712. It may also be constructed by projecting the Cantor cube onto the plane orthogonal to its main diagonal. A closely related fractal, the Sierpinski hexagon, is formed by repeatedly replacing each hexagon by six smaller hexagons, omitting the central seventh hexagon.. It is named after the work of Wacław Sierpiński and by analogy to the Sierpinski triangle, and has the same Koch snowflake exterior boundary as the hexaflake.
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The variety comes from various ways of forming the polyhedron that provides a base for the points—using an octagonal face instead of a square face, for example. The common original Herrnhut Moravian star becomes a 50-point star when the squares and triangles that normally make up the faces of the polyhedron become octagons and hexagons. This leaves a 4-sided trapezoidal hole in the corners of the faces which is then filled with an irregular four sided point. These 4-sided points form a "starburst" in the midst of an otherwise regular 26-point star.
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The objective of the game is for the player to form hexagons of a solid color (called a "Hex") by rotating into place and combining together colored triangles which drop down from the top of the screen. The player is required to create a certain number of Hexes in order to pass each stage. Initially the game starts with triangles encompassing only two colors, with more colors eventually being added to the mix. In addition, glowing triangles give the player power-ups such as creating a hole in the bottom of the play area, or swapping colors.
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Semesterberichte, Bd. 54, 2007, S. 53–68,Kotschick The topology and combinatorics of soccer balls, American Scientist, July/August 2006 In the case of the sphere, there is only the standard football (12 black pentagons, 20 white hexagons, with a pattern corresponding to an icosahedral root) provided that "precisely three edges meet at every vertex". If more than three faces meet at some vertex, then there is a method to generate infinite sequences of different soccer balls by a topological construction called a branched covering. Kotschick's analysis also applies to fullerenes and polyhedra that Kotschick calls generalized soccer balls.
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The tablet "demonstrates the greatest known computational accuracy obtained anywhere in the ancient world", the equivalent of six decimal digits of accuracy. Other Babylonian tablets include the computations of areas of hexagons and heptagons, which involve the approximation of more complicated algebraic numbers such as . The same number can also be used in the interpretation of certain ancient Egyptian calculations of the dimensions of pyramids. However, the much greater numerical precision of the numbers on YBC 7289 makes it more clear that they are the result of a general procedure for calculating them, rather than merely being an estimate.
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The game can be played by two, three or four players, with additional rules provided for solo and four-player partnership play. Each player has a rack of six randomly chosen tiles which are concealed from the other players. The board is also made up of a number of hexagons, with the two outermost rings reserved for three- and four-player games respectively. The rules state that the youngest player takes the first turn, although where multiple games are played it is common practice for the first turn to rotate clockwise around the board in subsequent games.
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By repeatedly removing leaves in this way, the Wiener index may be calculated in linear time.. For graphs that are constructed as products of simpler graphs, the Wiener index of the product graph can often be computed by a simple formula that combines the indices of its factors.. Benzenoids (graphs formed by gluing regular hexagons edge-to- edge) can be embedded isometrically into the Cartesian product of three trees, allowing their Wiener indices to be computed in linear time by using the product formula together with the linear time tree algorithm.. For earlier algorithms for benzenoids based on their partial cube structure, see .
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One of the manners they are bonded to each other in a succession of double-bonded silicons, analogous to the situation of carbon found in cumulene. The other manner they may be bonded to each other is a succession of alternating single and triple-bonded silicons, analogous to the situation of carbon found in polyyne. 2-dimensional silicyne is analogous to the carbon allotrope graphyne, and similar to the silicon allotrope silicene, being a sheet of silicon atoms. In this form, the silicyne chains that link the silicene hexagons use disilyne bonding alternating with disilane bonding, analogous to polyyne.
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Buckminsterfullerene is the smallest fullerene molecule containing pentagonal and hexagonal rings in which no two pentagons share an edge (which can be destabilizing, as in pentalene). It is also most common in terms of natural occurrence, as it can often be found in soot. The empirical formula of buckminsterfullerene is and its structure is a truncated icosahedron, which resembles an association football ball of the type made of twenty hexagons and twelve pentagons, with a carbon atom at the vertices of each polygon and a bond along each polygon edge. The van der Waals diameter of a buckminsterfullerene molecule is about 1.1 nanometers (nm).
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One exception is a depiction of the road to Calvary and the Crucifixion. The vaults of the passageways are decorated with coffers, some of which are hexagons, which may indicate the influence of Italian architect Sebastian Serlio. The Sala de Profundis, or meditation room, contains well-preserved multichromatic murals which depict a large number of saints including a series of martyrs and a depiction of Saint Augustine. These images are in the process of restoration by the Instituto Nacional de Antropología e Historia. In the south wing of the cloister there is an entrance to an underground area, which tradition says used to lead to Hernán Cortés’ house, but since destroyed.
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It is a chiral pattern, meaning that it is impossible to superpose it on top of its mirror image using only translations and rotations. A uniform tiling is a tiling in which each tile is a regular polygon and in which every vertex can be mapped to every other vertex by a symmetry of the tiling. Usually, uniform tilings additionally are required to have tiles that meet edge-to-edge, but if this requirement is relaxed then there are eight additional uniform tilings. Four are formed from infinite strips of squares or equilateral triangles, and three are formed from equilateral triangles and regular hexagons.
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Blockbusters is a British television quiz show based upon an American quiz show of the same name. A solo player and a team of two answer trivia questions, clued up with an initial letter of the answer, to complete a path across or down a game board of hexagons. The programme premiered on 29 August 1983 on ITV and ran for ten series, ending on the ITV network on 19 May 1993. It has since been revived for four additional series, the most recent of which was a comedy version hosted by Dara Ó Briain, which premiered on Comedy Central on 21 March 2019.
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The design of the artifact known as the Bush Barrow Lozenge, and the smaller lozenge, has been shown to be based on a hexagon construction. Both the shape and the decorative panels appear to have been created by repeating hexagons within a series of three concentric circles (each framing the series of smaller decorative panels).Johnson, Anthony, Solving Stonehenge: The New Key to an Ancient Enigma pp 182-185 (Thames & Hudson, 2008) The precision and accuracy displayed by the work demonstrates both a sophisticated tool kit and a sound knowledge of geometric form. A similar gold lozenge from Clandon Barrow, in Dorset, used a decagon in its design.
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Most Goldberg polyhedra can be constructed using Conway polyhedron notation starting with (T)etrahedron, (C)ube, and (D)odecahedron seeds. The chamfer operator, c, replaces all edges by hexagons, transforming GP(m,n) to GP(2m,2n), with a T multiplier of 4\. The truncated kis operator, y = tk, generates GP(3,0), transforming GP(m,n) to GP(3m,3n), with a T multiplier of 9\. For class 2 forms, the dual kis operator, z = dk, transforms GP(a,0) into GP(a,a), with a T multiplier of 3. For class 3 forms, the whirl operator, w, generates GP(2,1), with a T multiplier of 7.
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The Hexagonal-Ulam–Warburton cellular automaton (Hex-UWCA) is a 2-dimensional fractal pattern that grows on a regular grid of cells consisting of hexagons. The same growth rule for the UWCA applies and the pattern returns to a hexagon in generations n=2^k, when the first hexagon is considered as generation 1. The UWCA has two reflection lines that pass through the corners of the initial cell dividing the square into four quadrants, similarly the Hex-UWCA has three reflection lines dividing the hexagon into six sections and the growth rule follows the symmetries. Cells whose centers lie on a line of reflection symmetry are never born.
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The original Famicom Wars game consists of two armies, Red Star (which became Orange Star in later international versions, possibly to avoid associations with Communism) and Blue Moon fighting over square grid-based maps. The two armies could either be controlled by human players, or a human player could play against an AI opponent. The original Game Boy Wars games featured a system similar to Famicom Wars, except the grid was changed so that the grid squares acted more like hexagons; each square is adjacent to six other squares, instead of four. Game Boy Wars also features a different opposing army called White Moon.
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The Fevernova's colouring parted from the Tango's style of three-pointed shapes connecting each hexagon, instead introducing a different, triangle-like shape on four hexagons. This colourful and revolutionary look and colour usage was entirely based on Asian culture (the dark gold trigon resembles a tomoe and the red streaks on its angles resemble calligraphy brush strokes). It also featured a refined syntactic foam layer, to give the ball superior performance characteristics, and a three-layer knitted chassis, allowing for a more precise and predictable flight path. This ball was notoriously criticised for being too light, yet some spectacular goals were scored with it during the tournament.
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Order n=3 M = 38A magic hexagon of order n is an arrangement of numbers in a centered hexagonal pattern with n cells on each edge, in such a way that the numbers in each row, in all three directions, sum to the same magic constant M. A normal magic hexagon contains the consecutive integers from 1 to 3n2 − 3n + 1\. It turns out that normal magic hexagons exist only for n = 1 (which is trivial, as it is composed of only 1 hexagon) and n = 3\. Moreover, the solution of order 3 is essentially unique.Trigg, C. W. "A Unique Magic Hexagon", Recreational Mathematics Magazine, January–February 1964.
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The first player to complete his or her connection wins the game. The four corner hexagons each belong to both adjacent sides. It is not necessary to construct a complete chain between sides or fill up the whole board before the game is decided (but if it does by construction, the player placing the last stone will win); usually only 1/3 to 40% of the board is filled before it becomes obvious that one player or the other can force a win. This is somewhat analogous to chess games ending long before checkmate - the game usually ends with one player or the other resigning.
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The balls used in association football and team handball are perhaps the best-known example of a spherical polyhedron analog to the truncated icosahedron, found in everyday life. The ball comprises the same pattern of regular pentagons and regular hexagons, but it is more spherical due to the pressure of the air inside and the elasticity of the ball. This ball type was introduced to the World Cup in 1970 (starting in 2006, this iconic design has been superseded by alternative patterns). Geodesic domes are typically based on triangular facetings of this geometry with example structures found across the world, popularized by Buckminster Fuller.
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The computer always starts with more fame points than the human; since this state of affairs tends to produce an increasingly overwhelming materiel advantage if left unaddressed, the goal of depleting the computer's fame points, usually by destroying powerful red Army units, tends to be a high priority at the beginning of the game. The hexagons can be plains, woods, mountains, barren terrain, shoals, seas, bridges, airports, towns, or factories. The terrain in each hexagon has an effect on maneuverability and the extent to which forces can take evasive action. Units can be repaired, refueled, and rearmed at cities or airports, depending on whether the unit is a ground or air unit.
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Although the original cell towers created an even, omnidirectional signal, were at the centers of the cells and were omnidirectional, a cellular map can be redrawn with the cellular telephone towers located at the corners of the hexagons where three cells converge. Each tower has three sets of directional antennas aimed in three different directions with 120 degrees for each cell (totaling 360 degrees) and receiving/transmitting into three different cells at different frequencies. This provides a minimum of three channels, and three towers for each cell and greatly increases the chances of receiving a usable signal from at least one direction. The numbers in the illustration are channel numbers, which repeat every 3 cells.
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A type of buckyball which uses boron atoms, instead of the usual carbon, was predicted and described in 2007. The structure, with each atom forming 5 or 6 bonds, is predicted to be more stable than the buckyball. One reason for this given by the researchers is that is actually more like the original geodesic dome structure popularized by Buckminster Fuller, which uses triangles rather than hexagons. However, this work has been subject to much criticism by quantum chemists as it was concluded that the predicted Ih symmetric structure was vibrationally unstable and the resulting cage undergoes a spontaneous symmetry break, yielding a puckered cage with rare Th symmetry (symmetry of a volleyball).
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Philip T. Porter, also of Bell Labs, proposed that the cell towers be at the corners of the hexagons rather than the centers and have directional antennas that would transmit/receive in 3 directions (see picture at right) into 3 adjacent hexagon cells.interview of Joel S. Engel, page 17 (image 18) The technology did not exist then and the radio frequencies had not yet been allocated. Cellular technology was undeveloped until the 1960s, when Richard H. Frenkiel and Joel S. Engel of Bell Labs developed the electronics. Meanwhile, the 1956 inauguration of the TAT-1 cable and later international direct dialing were important steps in putting together the various continental telephone networks into a global network.
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The Lemoine hexagon is a cyclic hexagon (one inscribed in a circle) with vertices given by the six intersections of the edges of a triangle and the three lines that are parallel to the edges that pass through its symmedian point. If the successive sides of a cyclic hexagon are a, b, c, d, e, f, then the three main diagonals intersect in a single point if and only if .Cartensen, Jens, "About hexagons", Mathematical Spectrum 33(2) (2000–2001), 37–40. If, for each side of a cyclic hexagon, the adjacent sides are extended to their intersection, forming a triangle exterior to the given side, then the segments connecting the circumcenters of opposite triangles are concurrent.
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They also nested size relations within these classes, choosing for example large star, middle sized star, small star, large hexagon, middle sized hexagon, etc. At the end of their training the monkeys were able to simultaneously maintain 4 different sequences that randomly alternated on different trials: 9 stars ordered by size, 9 hexagons ordered by size and 9 triangles ordered by size, as well as a 9 item set composed of all three shapes – also ordered by size. This is the first example of the acquisition of a complex hierarchical structure by a non- human primate and has been cited by Hauser and McDermott (2003) as a possible exception to the claim that only humans have "infinite productivity".
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The Bingel reaction in fullerene chemistry is a fullerene cyclopropanation reaction to a methanofullerene first discovered by C. Bingel in 1993 with the bromo derivative of diethyl malonate in the presence of a base such as sodium hydride or DBU. The preferred double bonds for this reaction on the fullerene surface are the shorter bonds at the junctions of two hexagons (6-6 bonds) and the driving force is relief of steric strain. The reaction is of importance in the field of chemistry because it allows the introduction of useful extensions to the fullerene sphere. These extensions alter their properties, for instance solubility and electrochemical behavior, and therefore widen the range of potential technical applications.
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The landscape in this parish is different from the rest of the landscape in County Limerick which is predominantly flat. This is because Kilteely-Dromkeen is situated in one of the most important Carboniferous Volcanic districts in either Great Britain or Ireland. A variety of igneous rocks from two volcanic phases of about 300 million years ago can be found here. The volcanic plugs of Knockderk 220 m (782 ft) and Kilteely Hill 176 m (580 ft) are both conical in appearance, while in the neighbouring parish of Pallasgreen stands the Hill of Nicker, where hardened lavas have formed a cliff of basalt hexagons, similar to those found at the Giant's Causeway.
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The existence of the giant Moiré pattern in graphene nanoribbon (GNR) embedded in hBN indicates that the graphene was highly crystalline and precisely aligned with the h-BN underneath. It was noticed that the Moiré pattern appeared to be stretched along the GNR, while it appeared relaxed laterally. This trend differs from regular hexagons with a periodicity of ∼14 nm, which have always been observed with well-aligned graphene domains on h-BN. This observation gives a strong indication of the in-plane epitaxy between the graphene and the h-BN at the edges of the trench, where the graphene is stretched by tensile strain along the ribbon, due to a lattice mismatch between the graphene and h-BN.
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Although the procedure for the synthesis of the C60 fullerene is well established (generation of a large current between two nearby graphite electrodes in an inert atmosphere) a 2002 study described an organic synthesis of the compound starting from simple organic compounds.The numbers in image correspond to the way the new carbon carbon bonds are formed. :Multistep fullerene synthesis In the final step a large polycyclic aromatic hydrocarbon consisting of 13 hexagons and three pentagons was submitted to flash vacuum pyrolysis at 1100 °C and 0.01 Torr. The three carbon chlorine bonds served as free radical incubators and the ball was stitched up in a no-doubt complex series of radical reactions.
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16×8-grid showing the 128 states of a seven-segment display The seven elements of the display can be lit in different combinations to represent the Arabic numerals. Often the seven segments are arranged in an oblique (slanted) arrangement, which aids readability. In most applications, the seven segments are of nearly uniform shape and size (usually elongated hexagons, though trapezoids and rectangles can also be used), though in the case of adding machines, the vertical segments are longer and more oddly shaped at the ends in an effort to further enhance readability. The seven segments are arranged as a rectangle of two vertical segments on each side with one horizontal segment on the top, middle, and bottom.
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As a result of origami study through the application of geometric principles, methods such as Haga's theorem have allowed paperfolders to accurately fold the side of a square into thirds, fifths, sevenths, and ninths. Other theorems and methods have allowed paperfolders to get other shapes from a square, such as equilateral triangles, pentagons, hexagons, and special rectangles such as the golden rectangle and the silver rectangle. Methods for folding most regular polygons up to and including the regular 19-gon have been developed. A regular n-gon can be constructed by paper folding if and only if n is a product of distinct Pierpont primes, powers of two, and powers of three.
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The number of sides of each face is twice the number of lines that cross in the arrangement. For instance, the elongated dodecahedron shown is a zonohedron with five generators, two pairs of opposite hexagon faces, and four pairs of opposite parallelogram faces. In the corresponding five-line arrangement, two triples of lines cross (corresponding to the two pairs of opposite hexagons) and the remaining four pairs of lines cross at ordinary points (corresponding to the four pairs of opposite parallelograms). An equivalent statement of the Sylvester–Gallai theorem, in terms of zonohedra, is that every zonohedron has at least one parallelogram face (counting rectangles, rhombuses, and squares as special cases of parallelograms).
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Fresnedo Siri designed a dramatic spider web-like steel structure to support the building, allowing the entire interior space to be free of any supporting columns.The steel for the spider-web like structure that sustains the cylindrical conference center came from Mimsco Steel Corporation of Lorton, VA and was erected by the Heron Todd Steel Construction Company of Arlington, VA (source: The Washington Evening Star, October 30, 1964, p. F-1) The resulting internal space, naturally lit by windows throughout the cylinder's full 360 degrees, achieves an impressive sense of openness and purity of design. The cylindrical building is encased on the outside by a lattice-like grill of diamond-shaped hexagons composed of white marble, quartz and Portland cement.
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San Carlo alle Quattro Fontane. A Study in Multiple Form and Architectural Symbolism, New York, 1977 The dome with its intricate geometrical pattern The pendentives are part of the transition area where the undulating almost cross-like form of the lower order is reconciled with the oval opening to the dome. The arches which spring from the diagonally placed columns of the lower wall order to frame the altars and entrance, rise to meet the oval entablature and so define the space of the pendentives in which roundels are set. The oval entablature to the dome has a 'crown' of foliage and frames a view of deep set interlocking coffering of octagons, crosses and hexagons which diminish in size the higher they rise.
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In 1972, while residing in India after spells in Borneo, Nepal and South America, she sought a new project after she had run out of yarn. Beyer was given a Grandmother's Flower Garden quilt pattern, and cut her first quilt into 600 hexagons of Indrian fabrics in the colors dark blue and deep red. Upon returning to the United States, she learned quilting on the top and binding; Beyer was unable to locate another quilter before she came across a meeting held by Hazel Carter near her residence, and showed them a navy-colored Indian Grandmother's Flower Garden quilt top, which they praised. Carter encouraged Beyer to enter the 1976 Quilter's Newsletter Magazine's Bicentennial Quilt Contest, which she won with her red, white, and blue Bicentennial Quilt.
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There is also the question of whether any sufficiently large set of points in general position has an "empty" convex quadrilateral, pentagon, etc., that is, one that contains no other input point. The original solution to the happy ending problem can be adapted to show that any five points in general position have an empty convex quadrilateral, as shown in the illustration, and any ten points in general position have an empty convex pentagon.. However, there exist arbitrarily large sets of points in general position that contain no empty convex heptagon. For a long time the question of the existence of empty hexagons remained open, but and proved that every sufficiently large point set in general position contains a convex empty hexagon.
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The Möbius–Kantor graph, embedded on the torus. Edges extending upwards from the central square should be viewed as connecting with the corresponding edge extending downwards from the square, and edges extending leftwards from the square should be viewed as connecting with the corresponding edge extending rightwards. The Möbius–Kantor graph cannot be embedded without crossings in the plane; it has crossing number 4, and is the smallest cubic graph with that crossing number . Additionally, it provides an example of a graph all of whose subgraphs' crossing numbers differ from it by two or more.. However, it is a toroidal graph: it has an embedding in the torus in which all faces are hexagons . The dual graph of this embedding is the hyperoctahedral graph K2,2,2,2.
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Middle stage patterns on geometric borders around a alt=Middle stage Islamic patterns The next development, marking the middle stage of Islamic geometric pattern usage, was of 6- and 8-point stars, which appear in 879 at the Ibn Tulun Mosque, Cairo, and then became widespread. A wider variety of patterns were used from the 11th century. Abstract 6- and 8-point shapes appear in the Tower of Kharaqan at Qazvin, Persia in 1067, and the Al-Juyushi Mosque, Egypt in 1085, again becoming widespread from there, though 6-point patterns are rare in Turkey. In 1086, 7- and 10-point girih patterns (with heptagons, 5- and 6-pointed stars, triangles and irregular hexagons) appear in the Jameh Mosque of Isfahan.
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One of the ways of making a dodecagon with pattern blocks Pattern blocks consist of various wooden shapes (green triangles, red trapezoids, yellow hexagons, orange squares, tan (long) rhombi, and blue (wide) rhombi) that are sized in such a way that students will be able to see relationships among shapes. For example, three green triangles make a red trapezoid; two red trapezoids make up a yellow hexagon; a blue rhombus is made up of two green triangles; three blue rhombi make a yellow hexagon, etc. Playing with the shapes in these ways help children develop a spatial understanding of how shapes are composed and decomposed, an essential understanding in early geometry. Pattern blocks are also used by teachers as a means for students to identify, extend, and create patterns.
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For instance, the complete graph is a toroidal graph: it is not planar but can be embedded in a torus, with each face of the embedding being a triangle. This embedding has the Heawood graph as its dual graph.. The same concept works equally well for non- orientable surfaces. For instance, can be embedded in the projective plane with ten triangular faces as the hemi-icosahedron, whose dual is the Petersen graph embedded as the hemi-dodecahedron.. Even planar graphs may have nonplanar embeddings, with duals derived from those embeddings that differ from their planar duals. For instance, the four Petrie polygons of a cube (hexagons formed by removing two opposite vertices of the cube) form the hexagonal faces of an embedding of the cube in a torus.
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The book is organized in chapters related to various soccer subjects ("The ball", "The field", "The player", etc.). Inside each chapter we find the answers to questions such as what it would be like to play soccer in each of the planets of the Solar System, why the ball is more than one meter ahead of where we think it really is in a 100 km/h kick (due to delays in the transmission of the nervous impulse), or why soccer balls are made of 12 pentagons and 20 hexagons, etc. This book is also available in e-reader format. Introduction to BioMEMS (CRC Press, 2012) covers the whole breadth of BioMEMS (Biomedical MicroElectroMechanicalSystems), including classical microfabrication, microfluidics, tissue engineering, cell-based and noncell- based devices, and implantable systems.
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Screens made up of labyrinths of complicated joinery, consisting of multitudes of tiny balusters connecting hexagons, squares or other forms, with the flat surfaces constantly enriched with small carvings, are familiar to every one. In Cairo we also have examples in the mosque of Qous (12th century) of that finely arranged geometrical interlacing of curves with foliage terminations which distinguishes the Saracenic designer. Six panels in the Victoria and Albert Museum (13th century), and work on the tomb of the sultan Li Ghoury (16th century), show how deeply this form of decoration was ingrained in the Arab nature. Figure work and animals were sometimes introduced, in medieval fashion, as in the six panels just referred to, and at the hflpital du Moristan (13th century) and the mosque of El Nesfy Qeycoun (14th century).
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Then the Harris inequality says that these events are positively correlated: \Pr(a \leftrightarrow b,\ c\leftrightarrow d) \geq \Pr(a \leftrightarrow b)\Pr(c\leftrightarrow d). In other words, assuming the presence of one path can only increase the probability of the other. Similarly, if we randomly color the hexagons inside an n\times n rhombus-shaped hex board, then the events that there is black crossing from the left side of the board to the right side is positively correlated with having a black crossing from the top side to the bottom. On the other hand, having a left-to-right black crossing is negatively correlated with having a top-to-bottom white crossing, since the first is an increasing event (in the amount of blackness), while the second is decreasing.
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Piero della Francesca's image of a truncated icosahedron from his book De quinque corporibus regularibus The truncated icosahedron was known to Archimedes, who classified the 13 Archimedean solids in a lost work. All we know of his work on these shapes comes from Pappus of Alexandria, who merely lists the numbers of faces for each: 12 pentagons and 20 hexagons, in the case of the truncated icosahedron. The first known image and complete description of a truncated icosahedron is from a rediscovery by Piero della Francesca, in his 15th-century book De quinque corporibus regularibus, which included five of the Archimedean solids (the five truncations of the regular polyhedra). The same shape was depicted by Leonardo da Vinci, in his illustrations for Luca Pacioli's plagiarism of della Francesca's book in 1509.
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Buckminsterfullerene, C60 In 1985, on the basis of the Sussex studies and the stellar discoveries, laboratory experiments (with co- workers James R. Heath, Sean C. O'Brien, Yuan Liu, Robert Curl and Richard Smalley at Rice University) which simulated the chemical reactions in the atmospheres of the red giant stars demonstrated that stable C60 molecules could form spontaneously from a condensing carbon vapour. The co-investigators directed lasers at graphite and examined the results. The C60 molecule is a molecule with the same symmetry pattern as a football, consisting of 12 pentagons and 20 hexagons of carbon atoms. Kroto named the molecule buckminsterfullerene, after Buckminster Fuller who had conceived of the geodesic domes, as the dome concept had provided a clue to the likely structure of the new species.
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Chávez's music does not fall into clear stylistic periods, but rather cumulates elements in a process of continual synthesis. The juvenilia, up to 1921 and consisting primarily of piano compositions, is essentially Romantic, with Robert Schumann as the main influence. A period of nationalistic leanings was initiated in 1921 with the Aztec-themed ballet (The New Fire), followed by a second ballet, (The Four Suns), in 1925 . During his time in New York City between 1924 and 1928, Chávez acquired a taste for the then-fashionable abstract and quasi-scientific music, as is reflected in the titles of many of his compositions written between 1923 and 1934: for piano (Polygons, 1923), for voice and piano (Hexagons, 1924), 36 for piano (1925), for nine instruments (Energy, 1925), for violin and piano (Spiral, 1934), and an unfinished orchestral score titled (Pyramids).
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The Adidas Telstar became the standard design for representing footballs in different media Law 2 of the game specifies that the ball is an air-filled sphere with a circumference of , a weight of , inflated to a pressure of 0.6 to 1.1 atmospheres () "at sea level", and covered in leather or "other suitable material". The weight specified for a ball is the dry weight, as older balls often became significantly heavier in the course of a match played in wet weather. The standard ball is a Size 5, although smaller sizes exist: Size 3 is standard for team handball and Size 4 in futsal and other small-field variants. Other sizes are used in underage games or as novelty items. Most modern footballs are stitched from 32 panels of waterproofed leather or plastic: 12 regular pentagons and 20 regular hexagons.
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Ronald Weeks presented many potential shapes and forms for the basic ground plan: one like a conch shell; a fan-shaped plan (rejected as it covered the whole of the available site); a circular plan; a coil-shaped plan, and a helix-shaped plan with great concrete beams in a swirling staircase reaching into the sky.Ronald Weeks, 'The Design and Construction of the Cathedral Church of SS. Peter & Paul, Clifton', 1973, Pax Autumn/Winter 1973, pp60-69, quote p62 The final design was based on groups of hexagons. For Ronald Weeks the ‘architecture then flowed logically form the functions, ...moulded in three dimensions to create the internal environment.' The arrangement of the different parts of the church placed those of least (liturgical) importance on the periphery leading progressively to the more important elements and to the High Altar.
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Reptiles depicts a desk upon which is a 2D drawing of a tessellated pattern of reptiles and hexagons, Escher's 1939 Regular Division of the Plane. The reptiles at one edge of the drawing emerge into three dimensional reality, come to life and appear to crawl over a series of symbolic objects (a book on nature, a geometer's triangle, a three dimensional dodecahedron, a pewter bowl containing a box of matches and a box of cigarettes) to eventually re-enter the drawing at its opposite edge. Other objects on the desk are a potted cactus and yucca, a ceramic flask with a cork stopper next to a small glass of liquid, a book of JOB cigarette rolling papers, and an open handwritten note book of many pages. Although only the size of small lizards, the reptiles have protruding crocodile-like fangs, and the one atop the dodecahedron has a dragon-like puff of smoke billowing from its nostrils.
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Its three-part name derives from its key features: "flow-following" indicates that its vertical coordinates are based on both terrain and potential temperature (isentropic sigma coordinates, previously used in the now-discontinued rapid update cycle model), and "finite-volume" describes the method used for calculating horizontal transport. The "icosahedral" portion describes the model's most uncommon feature: whereas most grid-based forecast models have historically used rectangular grid points (a less than ideal arrangement for a planet that is a slightly oblate spheroid), the FIM instead fits Earth to a Goldberg polyhedron with icosahedral symmetry, with twelve evenly spaced pentagons (including two at the poles) anchoring a grid of hexagons. In November 2016, the ESRL announced it was no longer pursuing the FIM as a replacement for the GFS and would be instead developing the FV3, which uses some of the FIM's principles except on a square grid. The FIM will continue to be run for experimental purposes until FV3 commences.
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Coxeter explained in 1937 how he and Petrie began to expand the classical subject of regular polyhedra: :One day in 1926, J. F. Petrie told me with much excitement that he had discovered two new regular polyhedral; infinite but free of false vertices. When my incredulity had begun to subside, he described them to me: one consisting of squares, six at each vertex, and one consisting of hexagons, four at each vertex.H.S.M. Coxeter (1937) "Regular skew polyhedral in three and four dimensions and their topological analogues", Proceedings of the London Mathematical Society (2) 43: 33 to 62 In 1938 Petrie collaborated with Coxeter, Patrick du Val, and H.T. Flather to produce The Fifty-Nine Icosahedra for publication.H. S. M. Coxeter, Patrick du Val, H.T. Flather, J.F. Petrie (1938) The Fifty-nine Icosahedra, University of Toronto studies, mathematical series 6: 1–26 Realizing the geometric facility of the skew polygons used by Petrie, Coxeter named them after his friend when he wrote Regular Polytopes.
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The authors argued that both species were evincing rational choice based on linear ordering of information and later confirmed this using reaction time measures. In his research, Brendan was concerned to allow monkeys long-term learning opportunities comparable to that available for children, and so his subsequent work with Cebus apella was a long and staged programme in which the monkeys were trained to seriate by size and classify by shape and colour up to 12 objects on a touch screen – a level of ordering competence that only emerges in human development at around 6/7 years of age and had never before been demonstrated in a non-human species. The sequences achieved by Cebus apella have significance for the evolution of human language. Although the monkeys were trained on a core spine such as square, circle, triangle, they transferred to extended versions such as "touch all the stars, then all the triangles, then all the hexagons" with an ease that could not be predicted by simple association learning.
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