A family of regular polytopes of order $4p^m$ with type $\{p, 2p\}$

TL;DR

This paper constructs infinite families of regular polytopes with specific symmetry properties, expanding the understanding of automorphism groups of polytopes of order $4p^m$ for odd primes.

Contribution

It introduces new infinite families of regular polytopes with automorphism groups of order $4p^m$, specifically for type p, 2p, where $p$ is an odd prime.

Findings

Constructed groups of order $4p^m$ as automorphism groups.

Identified polytopes with type p, 2p.

Special case: for $p=3$, polytopes are regular toroidal maps {3,6}.

Abstract

In this paper, we construct an infinite families of group $G$ of order $4p^m$ which can be an automorphism group of some regular polytope with type $\{p, 2p\}$, where $m \geq 3$ and $p$ is an odd prime. For $p=3$, our polytopes are the regular toroidal maps $\{3, 6\}$.