Constructing Self-Dual Chiral Polytopes

TL;DR

This paper introduces a method to construct self-dual chiral polytopes using the mixing construction, addressing the scarcity of known examples and expanding the toolkit for creating polytopes with specific properties.

Contribution

It presents a novel construction technique for self-dual chiral polytopes, enhancing the ability to generate examples with desired symmetry properties.

Findings

Demonstrates how to build self-dual chiral polytopes

Expands the set of known chiral polytope constructions

Provides a systematic method for creating polytopes with specific symmetries

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.