Quasiperiodic tiling

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A quasiperiodic tiling is a tiling of the plane that exhibits local periodicity under some transformations: every finite subset of its tiles reappears infinitely often throughout the tiling, but there is no nontrivial way of superimposing the whole tiling onto itself so that all tiles overlap perfectly.

Tessellation tiling of a plane using one or more geometric shapes, called tiles, with no overlaps and no gaps

A tessellation of a flat surface is the tiling of a plane using one or more geometric shapes, called tiles, with no overlaps and no gaps. In mathematics, tessellations can be generalized to higher dimensions and a variety of geometries.

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Aperiodic tiling non-periodic tiling with the additional property that it does not contain arbitrarily large periodic patches

An aperiodic tiling is a non-periodic tiling with the additional property that it does not contain arbitrarily large periodic patches. A set of tile-types is aperiodic if copies of these tiles can form only non-periodic tilings. The Penrose tilings are the best-known examples of aperiodic tilings.

Penrose tiling non-periodic tiling of the plane

A Penrose tiling is an example of non-periodic tiling generated by an aperiodic set of prototiles. Penrose tilings are named after mathematician and physicist Roger Penrose, who investigated these sets in the 1970s. The aperiodicity of prototiles implies that a shifted copy of a tiling will never match the original. A Penrose tiling may be constructed so as to exhibit both reflection symmetry and fivefold rotational symmetry, as in the diagram at the right.

Quasicrystal Chemical structure

A quasiperiodic crystal, or quasicrystal, is a structure that is ordered but not periodic. A quasicrystalline pattern can continuously fill all available space, but it lacks translational symmetry. While crystals, according to the classical crystallographic restriction theorem, can possess only two, three, four, and six-fold rotational symmetries, the Bragg diffraction pattern of quasicrystals shows sharp peaks with other symmetry orders, for instance five-fold.

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Cuboctahedron Archimedean solid

In geometry, a cuboctahedron is a polyhedron with 8 triangular faces and 6 square faces. A cuboctahedron has 12 identical vertices, with 2 triangles and 2 squares meeting at each, and 24 identical edges, each separating a triangle from a square. As such, it is a quasiregular polyhedron, i.e. an Archimedean solid that is not only vertex-transitive but also edge-transitive. It is the only radially equilateral convex polyhedron.

Dominoes tile-based game

Dominoes is a family of tile-based games played with rectangular "domino" tiles. Each domino is a rectangular tile with a line dividing its face into two square ends. Each end is marked with a number of spots or is blank. The backs of the dominoes in a set are indistinguishable, either blank or having some common design. The domino gaming pieces make up a domino set, sometimes called a deck or pack. The traditional Sino-European domino set consists of 28 dominoes, featuring all combinations of spot counts between zero and six. A domino set is a generic gaming device, similar to playing cards or dice, in that a variety of games can be played with a set.

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Mahjong is a tile-based game that was developed in China during the Qing dynasty and has spread throughout the world since the early 20th century. It is commonly played by four players. The game and its regional variants are widely played throughout Eastern and South Eastern Asia and have become popular in Western countries too. The game has also been adapted into a widespread online entertainment. Similar to the Western card game rummy, Mahjong is a game of skill, strategy, and calculation and involves a degree of chance.

Scrabble is a word game in which two to four players score points by placing tiles bearing a single letter onto a board divided into a 15×15 grid of squares. The tiles must form words that, in crossword fashion, read left to right in rows or downward in columns, and be included in a standard dictionary or lexicon.

Slate A fine-grained, foliated, homogeneous, weakly metamorphic rock

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<i>Carcassonne</i> (board game) board game

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In 3D computer graphics, shown-surface determination is the process used to determine which surfaces and parts of surfaces are not visible from a certain viewpoint. A hidden-surface determination algorithm is a solution to the visibility problem, which was one of the first major problems in the field of 3D computer graphics. The process of hidden-surface determination is sometimes called hiding, and such an algorithm is sometimes called a hider. The analogue for line rendering is hidden-line removal. Hidden-surface determination is necessary to render an image correctly, so that one may not view features hidden behind the model itself, allowing only the naturally viewable portion of the graphic to be visible.

Euclidean tilings by convex regular polygons subdivision of the plane into polygons that are all regular

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Hexagonal tiling tiling of the plane by regular hexagons

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}.

Square tiling tiling of the plane by squares

In geometry, the square tiling, square tessellation or square grid is a regular tiling of the Euclidean plane. It has Schläfli symbol of {4,4}, meaning it has 4 squares around every vertex.

Triangular tiling tiling of the plane by equilateral triangles

In geometry, the triangular tiling or triangular tessellation is one of the three regular tilings of the Euclidean plane. Because the internal angle of the equilateral triangle is 60 degrees, six triangles at a point occupy a full 360 degrees. The triangular tiling has Schläfli symbol of {3,6}.

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