A new algorithm to classify chiral polytopes with a given automorphism group

TL;DR

This paper introduces a novel algorithm for classifying chiral polytopes with a specified automorphism group, leveraging a unique generator set to explore previously inaccessible polytopes.

Contribution

The paper presents a new algorithm utilizing a special generator set to compute all chiral polytopes with a given automorphism group, expanding the scope of computational classification.

Findings

Successfully computes all chiral polytopes for certain groups

Identifies a new set of generators characterizing the automorphism group

Enables classification of previously unreachable polytopes

Abstract

We present a new algorithm to compute all the chiral polytopes that have a given group $G$ as full automorphism group. This algorithm uses a new set of generators that characterize the group, all of them except one being involutions. It permits to compute all chiral polytopes of groups that were previously unreachable by other known algorithms.