Tight chiral polyhedra

TL;DR

This paper characterizes the Schl"afli symbols of tight chiral polyhedra, which are minimal flag configurations, and provides group presentations for their automorphism groups, advancing understanding of their structure.

Contribution

It fully characterizes the Schl"afli symbols of tight chiral polyhedra and offers automorphism group presentations for several families, a novel comprehensive analysis.

Findings

Complete characterization of tight chiral polyhedra's Schl"afli symbols

Automorphism group presentations for specific families

Identification of minimal flag configurations in chiral polyhedra

Abstract

A chiral polyhedron with Schl\"afli symbol $\{p, q\}$ is called tight if it has $2pq$ flags, which is the minimum possible. In this paper, we fully characterize the Schl\"afli symbols of tight chiral polyhedra. We also provide presentations for the automorphism groups of several families of tight chiral polyhedra.