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- Socolar–Taylor_tile abstract "The Socolar–Taylor tile is a single tile which is aperiodic on the Euclidean plane, meaning that it admits only non-periodic tilings of the plane, with rotations and reflections of the tile allowed. It is the first known example of a single aperiodic tile, or "einstein". The basic version of the tile is a simple hexagon, with printed designs to enforce a local matching rule, regarding how the tiles may be placed. This rule cannot be geometrically implemented in two dimensions while keeping the tile a connected set.This is, however, possible in three dimensions, and in their original paper Socolar and Taylor suggest a three-dimensional analogue to the monotile. The 3D monotile aperiodically tiles three-dimensional space; however, much as the structure of the 2D tile prevents it from being fitted together just by sliding the tiles together in 2D space, physical copies of the three-dimensional tile could not be fitted together without access to four-dimensional space. This tile is likewise the only known 3D aperiodic tile which can fill three-dimensional space unpredictably.".
- Socolar–Taylor_tile thumbnail Socolar-Taylor_3D_monotile.jpg?width=300.
- Socolar–Taylor_tile wikiPageID "39570044".
- Socolar–Taylor_tile wikiPageRevisionID "573365086".
- Socolar–Taylor_tile date "September 2013".
- Socolar–Taylor_tile few "September 2013".
- Socolar–Taylor_tile subject Category:Aperiodic_sets_of_tiles.
- Socolar–Taylor_tile subject Category:Tessellation.
- Socolar–Taylor_tile comment "The Socolar–Taylor tile is a single tile which is aperiodic on the Euclidean plane, meaning that it admits only non-periodic tilings of the plane, with rotations and reflections of the tile allowed. It is the first known example of a single aperiodic tile, or "einstein". The basic version of the tile is a simple hexagon, with printed designs to enforce a local matching rule, regarding how the tiles may be placed.".
- Socolar–Taylor_tile label "Socolar–Taylor tile".
- Socolar–Taylor_tile sameAs Socolar%E2%80%93Taylor_tile.
- Socolar–Taylor_tile sameAs Q17078320.
- Socolar–Taylor_tile sameAs Q17078320.
- Socolar–Taylor_tile wasDerivedFrom Socolar–Taylor_tile?oldid=573365086.
- Socolar–Taylor_tile depiction Socolar-Taylor_3D_monotile.jpg.