Description of reflection-generated polytopes using decorated Coxeter diagrams

Abstract

A new method of explicit description of n-dimensional polytopes generated by reflections of a single point (D-polytopes) or a face of maximal dimension (V-polytopes) is used to provide a comprehensive uniform description of all such polytopes in dimensions three and four. In addition a class of six-dimensional polytopes is also described; its symmetry group is the Weyl group of the simple Lie group D 6 .