Polytopes of finite type Original Research Article

This paper analyzes the polytopes whose types are the same as the types of finite (string) Coxeter groups. It is noted that the only polytopes of type {3,…,3} are the simplices, and shown that any quotient of the n-cube is a quotient by an elementary abelian 2-group. It is further noted that there are only two polytopes of type {3,5}, and computer searches reveal that there are 11 polytopes of type {3,3,5}, and 15 quotients of the universal polytope of type {3,4,3}, five of which themselves have that type. Only a few of these polytopes are regular, and none are chiral.