Coxeter diagram

Coxeter diagrams are a compact way of representing a wide variety of polytopes. They were devised by Harold Scott MacDonald Coxeter, but have been more recently generalized and reformatted by members of the Hi.gher.space forum.

A basic Coxeter diagram consists in a set of n nodes, ringed or unringed (x or o), with integers between them. The nodes represent (n–1)–dimensional hyperplanes, thought of as mirrors. A number k between two nodes indicates that the angle between their respective mirrors is π/k. A point can be placed somewhere between these mirror, at unit distance from the mirrors with ringed nodes, and inside the mirrors with unringed nodes. Reflecting this point over all mirrors will create the vertices of the polytope that the Coxeter diagram represents.