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Alternatively, an undecorated tile with no matching rules may be constructed, but the tile is not connected. The construction can be extended to a three-dimensional, connected tile with no matching rules, but this tile allows tilings that are periodic in one direction, and so it is only weakly aperiodic. Moreover, the tile is not simply connected.
In geometry, a tiling is a partition of the plane (or any other geometric setting) into closed sets (called tiles), without gaps or overlaps (other than the boundaries of the tiles). [1] A tiling is considered periodic if there exist translations in two independent directions which map the tiling onto itself.
Every triangle will have a vertical side if patternTransform="matrix(1 1 -1 1 9 -2)" is removed. Other example, append the following element 'path' to the 'pattern' as its last child ( juste avant </pattern>), and see notably the rectangular repeated pattern coded from M0 0 below: <path d="m0 47 97-56v112zm0 112l291-168v336z M0 0H388V672H0z"
A periodic tiling has a repeating pattern. Some special kinds include regular tilings with regular polygonal tiles all of the same shape, and semiregular tilings with regular tiles of more than one shape and with every corner identically arranged. The patterns formed by periodic tilings can be categorized into 17 wallpaper groups. A tiling that ...
§2.1 Uniform tiling, Archimedean tiling, elongated triangular tiling, snub square tiling, truncated square tiling, truncated hexagonal tiling, trihexagonal tiling, snub trihexagonal tiling, rhombitrihexagonal tiling, §2.2 list of k-uniform tilings, demiregular tiling, 3-4-3-12 tiling, 3-4-6-12 tiling, 33344-33434 tiling, §2.3 k-isotoxal ...
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It is not difficult to design a set of tiles that admits non-periodic tilings as well as periodic tilings. (For example, randomly arranged tilings using a 2×2 square and 2×1 rectangle are typically non-periodic.) However, an aperiodic set of tiles can only produce non-periodic tilings.
In case where the initial triangle is isosceles, the midpoint of any segment in dashed red is a common vertex of four tiles with equal sizes: a = b, and each puzzle piece which is a quarter of a tile is an isosceles triangle. Whatever the shape of the initial triangle, the two assemblages of the five puzzle pieces have equal areas: a 2 + b 2 = c 2.
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