Abstract :
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.
