Tessellation

A tessellation of the plane is a collection of plane figures that fill the plane with no overlaps and no gaps.

One may also speak of tessellations of parts of the plane or of other surfaces. Generalizations to higher dimensions are also possible.

A regular tessellation is a tessellation made up of congruent regular polygons. Only three regular polygons can produce tessellations: triangles, squares, and hexagons.

Other types of tessellations are considered, depending on types of figures and types of pattern: regular vs. irregular, periodical vs. aperiodical, symmetric vs. asymmeric, fractal, etc.

Compare with the Penrose tiling, a tiling of two polygons that however create aperiodic patterns.

Etymological note

In Latin, tessella was a small cubical piece of clay, stone or glass used to make mosaics. The word "tessella" means "small square" (from "tessera", square, which in its turn is from the Greek word for "four").

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