Self-duality of chiral polytopes

摘要

We prove that self-dual chiral polytopes of odd rank possess a polarity, that is, an involutory duality, and give an example showing this is not true in even ranks. Properties of the extended groups, that is of the groups of automorphisms and dualities, of self-dual chiral polytopes are discussed in detail. (c) 2004 Elsevier Inc. All rights reserved.