Uniform polytope

Summary

A uniform polytope is a polytope whose symmetries can carry any vertex to any other vertex and whose facets are themselves uniform. In dimension two the uniform polytopes are the regular polygons. Every regular polytope is uniform, but uniform polytopes are far more numerous. In dimension three the convex ones are the Platonic solids, the thirteen Archimedean solids, and the infinite families of prisms and antiprisms. Most uniform polytopes arise from the Wythoff construction.