… In Section 3 we explain our method for constructing examples of chiral polytopes from …
self-dual chiral 4-polytopes in Section 4. Finally, we find small finite chiral 5-polytopes in Section 5. …

… Furthermore we remark that all sections of a chiral polytope must be directly regular or chiral
polytopes. In particular, the (n — 2)-faces and the co-faces at edges are directly regular (cf. […

… ", while regular apeirotope will mean" discrete faithfully realized abstract regular apeirotope";
we also adopt the corresponding terminology for chiral polytopes and chiral apeirotopes. …

… " and simply talk about chiral or directly regular polytopes whenever enantiomorphism is not
… our understanding of classes of chiral polytopes. Let ~t and ~2 be n-polytopes. Recall that if …

… there are no convex chiral polytopes, and we do not know of a natural family of chiral
polytopes providing an example in each rank. Consequently, several questions that have …

… Section 2 reviews the basics of abstract polytopes. In Section 3, we give the basics of … chiral
polytopes. We also explain how to get chiral polytopes as quotients of regular polytopes. In …

… In this paper we describe a construction for chiral polytopes with preassigned regular
facets. Furthermore we show that this construction implies the existence of chiral d -polytopes …

… We prove that self-dual chiral polytopes of odd rank possess a polarity, that is, an involutory
… of self-dual chiral polytopes are discussed in detail. © 2004 Elsevier Inc. All rights reserved. …

… An abstract polytope of rank n is said to be chiral if its automorphism group has precisely …
method for deriving new finite chiral polytopes from old finite chiral polytopes of the same rank. …

… Chiral polytopes are highly symmetric abstract polytopes that have maximal … chiral d-polytopes
with rank d ≥ 5 were known. In this paper we extend a construction for chiral 4-polytopes (…