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2. List of aperiodic sets of tiles - Wikipedia

   en.wikipedia.org/.../List_of_aperiodic_sets_of_tiles

   A tiling that cannot be constructed from a single primitive cell is called nonperiodic. If a given set of tiles allows only nonperiodic tilings, then this set of tiles is called aperiodic. [3] The tilings obtained from an aperiodic set of tiles are often called aperiodic tilings, though strictly speaking it is the tiles themselves that are ...

3. Penrose tiling - Wikipedia

   en.wikipedia.org/wiki/Penrose_tiling

   One approach is to color the vertices (with two colors, e.g., black and white) and require that adjacent tiles have matching vertices. [32] Another is to use a pattern of circular arcs (as shown above left in green and red) to constrain the placement of tiles: when two tiles share an edge in a tiling, the patterns must match at these edges. [21]

4. Aperiodic tiling - Wikipedia

   en.wikipedia.org/wiki/Aperiodic_tiling

   Robinson proves these tiles must form this structure inductively; in effect, the tiles must form blocks which themselves fit together as larger versions of the original tiles, and so on. This idea – of finding sets of tiles that can only admit hierarchical structures – has been used in the construction of most known aperiodic sets of tiles ...

5. Lists of uniform tilings on the sphere, plane, and hyperbolic ...

   en.wikipedia.org/wiki/Lists_of_uniform_tilings...

   There are different notations for expressing these uniform solutions, Wythoff symbol, Coxeter diagram, and Coxeter's t-notation. Simple tiles are generated by Möbius triangles with whole numbers p,q,r, while Schwarz triangles allow rational numbers p,q,r and allow star polygon faces, and have overlapping elements.

6. Tile - Wikipedia

   en.wikipedia.org/wiki/Tile

   Floor tiles are commonly made of ceramic or stone, although recent technological advances have resulted in rubber or glass tiles for floors as well. Ceramic tiles may be painted and glazed. Small mosaic tiles may be laid in various patterns. Floor tiles are typically set into mortar consisting of sand, Portland cement and often a latex additive.

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