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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_tiling.svg?width=300.
- Socolar–Taylor_tile wikiPageExternalLink taylortiling.com.
- Socolar–Taylor_tile wikiPageExternalLink thing:2101.
- Socolar–Taylor_tile wikiPageID "39570044".
- Socolar–Taylor_tile wikiPageLength "3748".
- Socolar–Taylor_tile wikiPageOutDegree "7".
- Socolar–Taylor_tile wikiPageRevisionID "649325208".
- Socolar–Taylor_tile wikiPageWikiLink Aperiodic_tiling.
- Socolar–Taylor_tile wikiPageWikiLink Category:Aperiodic_tilings.
- Socolar–Taylor_tile wikiPageWikiLink Connected_space.
- Socolar–Taylor_tile wikiPageWikiLink Einstein_problem.
- Socolar–Taylor_tile wikiPageWikiLink Tessellation.
- Socolar–Taylor_tile wikiPageWikiLink Two-dimensional_space.
- Socolar–Taylor_tile wikiPageWikiLink File:Socolar-Taylor_tiling.svg.
- Socolar–Taylor_tile wikiPageWikiLinkText "Socolar–Taylor tile".
- Socolar–Taylor_tile wikiPageUsesTemplate Template:Gallery.
- Socolar–Taylor_tile wikiPageUsesTemplate Template:Reflist.
- Socolar–Taylor_tile wikiPageUsesTemplate Template:Tessellation.
- Socolar–Taylor_tile subject Category:Aperiodic_tilings.
- Socolar–Taylor_tile hypernym Tile.
- Socolar–Taylor_tile type Software.
- 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 Q17078320.
- Socolar–Taylor_tile sameAs m.0vxc_0r.
- Socolar–Taylor_tile sameAs Q17078320.
- Socolar–Taylor_tile wasDerivedFrom Socolar–Taylor_tile?oldid=649325208.
- Socolar–Taylor_tile depiction Socolar-Taylor_tiling.svg.
- Socolar–Taylor_tile isPrimaryTopicOf Socolar–Taylor_tile.
