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Tessellation in two dimensions, also called planar tiling, is a topic in geometry that studies how shapes, known as tiles, can be arranged to fill a plane without any gaps, according to a given set of rules. These rules can be varied. Common ones are that there must be no gaps between tiles, and that no corner of one tile can lie along the edge ...
A wallpaper group (or plane symmetry group or plane crystallographic group) is a mathematical classification of a two-dimensional repetitive pattern, based on the symmetries in the pattern. Such patterns occur frequently in architecture and decorative art, especially in textiles, tiles, and wallpaper. The simplest wallpaper group, Group p 1 ...
The same image, with colors of lower contrast, no longer displaying the illusion. The café wall illusion (also known as the Münsterberg illusion or the kindergarten illusion) is a geometrical-optical illusion in which the parallel straight dividing lines between staggered rows with alternating dark and light rectangles (such as bricks or ...
Aperiodic tiling with "Tile(1,1)". The tiles are colored according to their rotational orientation modulo 60 degrees. [1] ( Smith, Myers, Kaplan, and Goodman-Strauss) In plane geometry, the einstein problem asks about the existence of a single prototile that by itself forms an aperiodic set of prototiles; that is, a shape that can tessellate space but only in a nonperiodic way.
Mahjong tiles (Chinese: 麻將牌 or 麻雀牌; pinyin: májiàngpái; Cantonese Jyutping: maa4zoek3paai2; Japanese: 麻雀牌; rōmaji: mājanpai) are tiles of Chinese origin that are used to play mahjong as well as mahjong solitaire and other games. Although they are most commonly tiles, they may refer to playing cards with similar contents ...
New York City Subway tiles. Atlantic Avenue – Barclays Center station identification on the BMT Brighton Line platform. Many New York City Subway stations are decorated with colorful ceramic plaques and tile mosaics. Of these, many take the form of signs, identifying the station's location. Much of this ceramic work was in place when the ...
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Penrose tiling. A Penrose tiling is an example of an aperiodic tiling. Here, a tiling is a covering of the plane by non-overlapping polygons or other shapes, and a tiling is aperiodic if it does not contain arbitrarily large periodic regions or patches. However, despite their lack of translational symmetry, Penrose tilings may have both ...