Constructing self-dual chiral polytopes

Abstract

An abstract polytope is chiral if its automorphism group has two orbits on the flags, such that adjacent flags belong to distinct orbits. There are still few examples of chiral polytopes, and few constructions that can create chiral polytopes with specified properties. In this paper, we show how to build self-dual chiral polytopes using the mixing construction for polytopes.

Open problems on k-orbit polytopes

“…The mix of two regular or chiral polytopes (defined in [55,7]) constructs their minimal common cover. This is helpful for constructing chiral polytopes, as well as polytopes that are invariant under certain operations; see [7,13,15,59]. There is a natural candidate for the minimal common cover of two rooted polytopes:…”