Symmetry

A symmetry of a polytope is a distance-preserving transformation of its containing space that maps each of its elements to another element of the same type. Such transformations are called isometries. 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, with composition as its operation.

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