Regular polytope

Summary

A regular polytope is a polytope with the largest possible symmetry: its symmetries can carry any flag of faces to any other flag. In the plane the regular polytopes are the regular polygons, and in space the convex ones are the five Platonic solids. Each regular polytope is described by its Schläfli symbol, and their full list is given by the classification of regular polytopes. Regular polytopes are the model objects of the theory of polytopes and of finite reflection groups.