Tessellation

A tessellated plane seen in street brickwork.

Giant's Causeway in Northern Ireland.

Wallpaper of Painted porcelain, China

"a collection of plane figures that fills the plane with no overlaps and no gaps.... In Latin, tessella is a small cubical piece of clay, stone or glass used to make mosaics.^[1]"


"For an infinite tiling, let a be the average number of sides of a polygon, and b the average number of sides meeting at a vertex. Then (a − 2)(b − 2) = 4. For example, we have the combinations "

"Coxeter groups in the plane with equivalent diagrams. Domain mirrors are labeled as edge m1, m2, etc. Vertices are colored by their reflection order. The prismatic group [I^~₁xI^~₂] is shown as a doubling of the C^~₂, but can also be created as rectangular domains from doubling the H^~₂ triangles. The A^~₂ is a doubling of the H^~₂ triangle."http://en.wikipedia.org/wiki/Coxeter%E2%80%93Dynkin_diagram

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Example of wallpaper group type p4g. From ''The Grammar of Ornament'' (1856), by Owen Jones. Chinese No 1 (plate 59).