Mathematical notation | Polytopes | Polyhedra
Wythoff symbol
In geometry, the Wythoff symbol is a notation representing a Wythoff construction of a uniform polyhedron or plane tiling within a Schwarz triangle. It was first used by Coxeter, Longuet-Higgins and Miller in their enumeration of the uniform polyhedra. Later the Coxeter diagram was developed to mark uniform polytopes and honeycombs in n-dimensional space within a fundamental simplex. 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 3 | 2 4 with Oh symmetry, and 2 4 | 2 as a square prism with 2 colors and D4h symmetry, as well as 2 2 2 | with 3 colors and D2h symmetry. With a slight extension, Wythoff's symbol can be applied to all uniform polyhedra. However, the construction methods do not lead to all uniform tilings in Euclidean or hyperbolic space. (Wikipedia).
