• Thumbnail for Socolar tiling
    A Socolar tiling is an example of an aperiodic tiling, developed in 1989 by Joshua Socolar in the exploration of quasicrystals. There are 3 tiles a 30°...
    2 KB (261 words) - 19:05, 20 October 2024
  • Thumbnail for Socolar–Taylor tile
    The Socolar–Taylor tile is a single non-connected tile which is aperiodic on the Euclidean plane, meaning that it admits only non-periodic tilings of the...
    4 KB (423 words) - 12:14, 1 June 2025
  • Thumbnail for List of aperiodic sets of tiles
    the tiles). A tiling is considered periodic if there exist translations in two independent directions which map the tiling onto itself. Such a tiling is...
    38 KB (2,607 words) - 10:21, 26 May 2025
  • Thumbnail for Einstein problem
    Commons. Einstein tile's molecular analogs may be used to form chiral, two dimensional quasicrystals. Binary tiling, a weakly aperiodic tiling of the hyperbolic...
    11 KB (1,155 words) - 03:48, 27 May 2025
  • Thumbnail for Aperiodic tiling
    aperiodic tiling is a non-periodic tiling with the additional property that it does not contain arbitrarily large periodic regions or patches. A set of tile-types...
    30 KB (3,508 words) - 12:34, 5 March 2025
  • Thumbnail for Dodecagon
    Dodecagon (section Tiling)
    with other regular polygons in 4 ways: Here are 3 example periodic plane tilings that use regular dodecagons, defined by their vertex configuration: A skew...
    16 KB (1,250 words) - 07:58, 20 March 2025
  • Thumbnail for Anisohedral tiling
    anisohedral if it admits a tiling, but no such tiling is isohedral (tile-transitive); that is, in any tiling by that shape there are two tiles that are not equivalent...
    6 KB (652 words) - 02:07, 15 June 2024
  • Thumbnail for Pattern Blocks
    Deci-Blocks Twenty-First Century Pattern Blocks Attribute blocks Socolar tiling - aperiodic tilings which 3 of the pattern block shapes with specific rules of...
    8 KB (924 words) - 13:20, 19 April 2025
  • Thumbnail for Ammann–Beenker tiling
    In geometry, an Ammann–Beenker tiling is a nonperiodic tiling which can be generated either by an aperiodic set of prototiles as done by Robert Ammann...
    12 KB (1,506 words) - 17:34, 3 January 2025
  • Thumbnail for Isohedral figure
    tiling (m = 1) has congruent faces, either directly or reflectively, which occur in one or more symmetry positions. An m-hedral polyhedron or tiling has...
    16 KB (678 words) - 04:06, 30 August 2024
  • Thumbnail for Gyrobifastigium
    With a Single Tile Joshua E. S. Socolar and Joan M. Taylor, 2011 Senechal, Marjorie (1996), "7.2 The SCD (Schmitt–Conway–Danzer) tile", Quasicrystals...
    7 KB (685 words) - 09:49, 18 October 2024
  • Thumbnail for Paul Steinhardt
    'Forbidden' Quasicrystal". Discover Magazine. Retrieved July 25, 2021. Socolar, J.; Steinhardt, P.J. (1986). "Quasicrystals II: Unit Cell Configurations"...
    60 KB (6,565 words) - 05:45, 2 June 2025
  • Thumbnail for Salvatore Torquato
    E. S. Socolar, P. J. Steinhardt, and S. Torquato. Hyperuniformity of quasicrystals. Phys. Rev. B, 95:054119, 2017. E. C. O˘guz, J. E. S. Socolar, P. J...
    67 KB (7,364 words) - 03:31, 25 October 2024