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If a square tiling is shifted by the width of a tile, parallel to the sides of the tile, the result is the same pattern of tiles as before the shift. A shift (formally, a translation) that preserves the tiling in this way is called a period of the tiling. A tiling is called periodic when it has periods that shift the tiling in two different ...
In the 1987 book, Tilings and patterns, Branko Grünbaum calls the vertex-uniform tilings Archimedean, in parallel to the Archimedean solids. Their dual tilings are called Laves tilings in honor of crystallographer Fritz Laves. [1] [2] They're also called Shubnikov–Laves tilings after Aleksei Shubnikov. [3]
Socolar–Taylor tile: 1: E 2: 2010 [46] [47] Not a connected set. Aperiodic hierarchical tiling. No image: Wang tiles: 20426: E 2: 1966 [48] No image: Wang tiles: 104: E 2: 2008 [49] No image: Wang tiles: 52: E 2: 1971 [13] [50] Tiles enforce aperiodicity by forming an infinite hierarchy of square lattices. Wang tiles: 32: E 2: 1986 [51 ...
Following Grünbaum and Shephard (section 1.3), a tiling is said to be regular if the symmetry group of the tiling acts transitively on the flags of the tiling, where a flag is a triple consisting of a mutually incident vertex, edge and tile of the tiling. This means that, for every pair of flags, there is a symmetry operation mapping the first ...
Infinitely many different pentagons can form this pattern, belonging to two of the 15 families of convex pentagons that can tile the plane. Their tilings have varying symmetries; all are face-symmetric. One particular form of the tiling, dual to the snub square tiling, has tiles with the minimum possible perimeter among all pentagonal tilings ...
#3 When You Can't Decide Which Tile Or Stone Pattern To Use, So You Use All Of Them Image credits: Istoh We also asked Logan if he's partial to any photos that he's seen shared in the subreddit.