Wythoff construction

Summary

The Wythoff construction builds a polytope from a finite reflection group and a chosen point. One takes a point in the fundamental region of the group and reflects it in the mirrors over and over. The convex hull of all the images is the polytope. Choosing which mirrors the point lies on gives the regular polytopes, their truncations and most other uniform polytopes with the same symmetry. It ties the geometry of polytopes to the combinatorics of Coxeter groups.