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2. Einstein problem - Wikipedia

   en.wikipedia.org/wiki/Einstein_problem

   Aperiodic tiling with "Tile(1,1)". The tiles are colored according to their rotational orientation modulo 60 degrees. ( Smith, Myers, Kaplan, and Goodman-Strauss) In plane geometry, the einstein problem asks about the existence of a single prototile that by itself forms an aperiodic set of prototiles; that is, a shape that can tessellate space but only in a nonperiodic way.

3. Toynbee tiles - Wikipedia

   en.wikipedia.org/wiki/Toynbee_tiles

   These tiles were glued with a thicker layer of asphalt glue or sealant than older ones. [citation needed] Usage Deployment. Toynbee-tile enthusiast Justin Duerr claims to have once found and examined a newly installed tile. This new tile was wrapped in tar paper and placed on a busy street early in the morning. From this find and other evidence ...

4. Aperiodic tiling - Wikipedia

   en.wikipedia.org/wiki/Aperiodic_tiling

   An aperiodic tiling using a single shape and its reflection, discovered by David Smith. An 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 (or prototiles) is aperiodic if copies of these tiles can form only non- periodic tilings.

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6. Tessellation - Wikipedia

   en.wikipedia.org/wiki/Tessellation

   A tessellation or tiling is the covering of a surface, often a plane, using one or more geometric shapes, called tiles, with no overlaps and no gaps. In mathematics, tessellation can be generalized to higher dimensions and a variety of geometries. A periodic tiling has a repeating pattern. Some special kinds include regular tilings with regular ...

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