Wythoff Symbol

A symbolic representation of a polyhedron by reference to a tessellation of the surface of a sphere with spherical triangles. The symbol appears as a set of three numbers and a vertical bar, in one of the following arrangements:

p q r |,   p q | r ,   p | q r ,   | p q r .

In all cases, the three numbers denote a spherical triangle with angles π/p, π/q, π/r, whose corresponding vertices we label P, Q, and R. There are restrictions on which triads of numbers are allowed, in that a set of such triangles must form a tessellation of the sphere by repeated reflections. In the case of star polyhedra the tessellation is allowed to cover the surface multiple times.

The position of the vertical bar determines how the vertices of the polyhedron are found from the resulting tessellation:

External Links: Entry on MathWorld.