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Non-periodic tiling of the plane
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°
Socolar_tiling
Aperiodic 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
Socolar–Taylor_tile
Form of plane tiling without repeats at scale
non-periodic tiling is a tiling that does not have any translational symmetry. An aperiodic set of prototiles is a set of tile-types that can tile, but only
Aperiodic_tiling
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
List of aperiodic sets of tiles
List_of_aperiodic_sets_of_tiles
Question about single-shape aperiodic tiling
Binary tiling, a weakly aperiodic tiling of the hyperbolic plane with a single tile Schmitt–Conway–Danzer tile, in three dimensions Two tiles have the
Einstein_problem
Polygon with 12 edges
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
Dodecagon
Tiling forced to use inequivalent tile placements
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
Anisohedral_tiling
Mathematical manipulatives
Deci-Blocks Twenty-First Century Pattern Blocks Attribute blocks Socolar tiling - aperiodic tilings which 3 of the pattern block shapes with specific rules of
Pattern_Blocks
Non-periodic tiling of the plane
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
Ammann–Beenker_tiling
Generalisation of dice with identical faces
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
Isohedral_figure
Polyhedron formed by joining two prisms
S2CID 122006114; see Table III, line 26 Socolar, Joshua E. S.; Taylor, Joan M. (2011), Forcing Nonperiodicity With a Single Tile, arXiv:1009.1419. Senechal, Marjorie
Gyrobifastigium
American theoretical scientist
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
Salvatore_Torquato
American theoretical physicist (born 1952)
discovered a quasicrystalline Islamic tiling on the Darb-e Imam Shrine (1453 A.D.) in Isfahan, Iran constructed from girih tiles. In 2007, they deciphered the
Paul_Steinhardt
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