Wythoff symbol

In geometry, the Wythoff symbol represents a Wythoff construction of a uniform polyhedron or plane tiling, from a Schwarz triangle. It was first used by Coxeter, Longuet-Higgins and Miller in their enumeration of the uniform polyhedra.

A Wythoff symbol consists of three numbers and a vertical bar. It represents one uniform polyhedron or tiling, although the same tiling/polyhedron can have different Wythoff symbols from different symmetry generators. For example, the regular cube can be represented by ${\displaystyle 3\ |\ 4\ 2}$ with O_h symmetry, and ${\displaystyle 2\ 4\ |\ 2}$ as a square prism with 2 colors and D_4h symmetry, as well as ${\displaystyle 2\ 2\ 2\ |}$ with 3 colors and ${\displaystyle D_{2h}}$ symmetry.

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