Minimal covers of the prisms and antiprisms

TL;DR

This paper classifies regular minimal abstract polytopes that serve as covers for convex polyhedral prisms and antiprisms, detailing their structure and completing the enumeration for convex uniform polyhedra, with implications for string C-groups.

Contribution

It provides a comprehensive classification and enumeration of minimal covers for prisms and antiprisms, advancing the understanding of their topological and algebraic properties.

Findings

Classified all regular minimal abstract polytope covers for prisms and antiprisms.

Completed enumeration of such covers for convex uniform polyhedra.

Explored structural questions in the theory of string C-groups.

Abstract

This paper contains a classication of the regular minimal abstract polytopes that act as covers for the convex polyhedral prisms and antiprisms. It includes a detailed discussion of their topological structure, and completes the enumeration of such covers for convex uniform polyhedra. Additionally, this paper addresses related structural questions in the theory of string C-groups.