Generating polytopes from Coxeter groups

Abstract

The main goal of this thesis is to study finite reflection groups (Coxeter groups) W and to use these to generate polytopes in two and three dimensions. Such polytopes will be generated as the convex hull of the W-orbit through an initial point. We prove an efficient recipe for finding the stabilizer of an initial point, and examine several examples of such polytopes and illustrate how many vertices, edges and faces these polytopes have. At last we will illustrate how this information can be pictorially encoded on the marked Coxeter diagram for an initial point.