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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 ...
The pattern represented by every finite patch of tiles in a Penrose tiling occurs infinitely many times throughout the tiling. They are quasicrystals: implemented as a physical structure a Penrose tiling will produce diffraction patterns with Bragg peaks and five-fold symmetry, revealing the repeated patterns and fixed orientations of its tiles ...
In geometry, many uniform tilings on sphere, euclidean plane, and hyperbolic plane can be made by Wythoff construction within a fundamental triangle, (p q r), defined by internal angles as π/p, π/q, and π/r.
Variant of the Penrose hexagon-triangle tiles. Discovered in 2003 or earlier. Golden triangle tiles: 10: E 2: 2001 [27] [28] Date is for discovery of matching rules. Dual to Ammann A2. Socolar tiles: 3: E 2: 1989 [29] [30] [31] Tilings MLD from the tilings by the Shield tiles. Shield tiles: 4: E 2: 1988 [32] [33] [34] Tilings MLD from the ...
Truchet tiles are square tiles decorated with patterns so they do not have rotational symmetry; in 1704, Sébastien Truchet used a square tile split into two triangles of contrasting colours. These can tile the plane either periodically or randomly. [46] [47] An einstein tile is a single shape that forces aperiodic tiling. The first such tile ...
Robinson proves these tiles must form this structure inductively; in effect, the tiles must form blocks which themselves fit together as larger versions of the original tiles, and so on. This idea – of finding sets of tiles that can only admit hierarchical structures – has been used in the construction of most known aperiodic sets of tiles ...
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The herringbone pattern has a symmetry of wallpaper group pgg, as long as the blocks are not of different color (i.e., considering the borders alone). Herringbone patterns can be found in wallpaper, mosaics, seating, cloth and clothing (herringbone cloth), shoe tread, security printing, herringbone gears, jewellery, sculpture, and elsewhere.