A recursive description of automorphism groups of inductively constructed polytopes

TL;DR

This paper computes the automorphism groups of a family of inductively constructed polytopes by leveraging Gleason and Hubard's prime factorisation theorem, providing insights into their symmetrical properties.

Contribution

It introduces a method to determine automorphism groups of inductively constructed polytopes using their unique prime factorisation.

Findings

Automorphism groups are explicitly computed for the studied polytopes.

Prime factorisation theorem is effectively applied to automorphism group analysis.

Results enhance understanding of symmetry in inductively constructed polytopes.

Abstract

Polytopes are ubiquitous in different areas of mathematics. Gleason and Hubard established a factorisation theorem, stating that every abstract polytope has a unique factorisation into prime polytopes. We compute the automorphism group of a certain family of inductively constructed polytopes using the unique factorisation.