Quasi-Regular Polytopes of Full Rank.

A polytope P in some euclidean space is called quasi-regular if each facet F of P is regular and the symmetry group G (F) of F is a subgroup of the symmetry group G (P) of P . Further, P is of full rank if its rank and dimension are the same. In this paper, the quasi-regular polytopes of full rank that are not regular are classified. Similarly, an apeirotope of full rank sits in a space of one fewer dimension; the discrete quasi-regular apeirotopes that are not regular are also classified here. One curiosity of the classification is the difference between even and odd dimensions, in that certain families are present in E d if d is even, but are absent if d is odd. [ABSTRACT FROM AUTHOR]