Symmetry

A symmetry of a polytope is a transformation of its containing space that maps each element of the polytope to another equivalent element of the polytope. For example, rotating a square 90° around its center is a symmetry. The symmetry group of a polytope is the group formed by the symmetries of a polytope and composition.

Reflection groups
An important subclass of the polytope symmetry groups is the class of reflection groups, which are symmetry groups generated by their reflections. Reflection groups can be represented using Coxeter diagrams.