Regular 3-polytopes of order 2đđ
Year: 2025
Type: article
Abstract: In a paper from 2006, Schulte and Weiss initiated the problem of characterizing the regular polytopes of orders 2 n ⢠p 2^{n}p for đ a positive integer and đ an odd prime. In this paper, we first prove that if a 3-polytope of order 2 n ⢠p 2^{n}p has Schläfli type { k 1 , k 2 } \{k_{1},k_{2}\} , then p ⣠k 1 p\mid k_{1} or p ⣠k 2 p\mid k_{2} . This leads to two classes, up to duality, for the Schläfli type, namely Type (1) where k 1 = 2 s ⢠p k_{1}=2^{s}p and k 2 = 2 t k_{2}=2^{t} and Type (2) where k 1 = 2 s ⢠p k_{1}=2^{s}p and k 2 = 2 t ⢠p k_{2}=2^{t}p . We then show that there exists a regular 3-polytope of order 2 n ⢠p 2^{n}p with Type (1) when
Source: Journal of Group Theory
Authors: Dong-Dong Hou, Yan-Quan Feng, Dimitri Leemans
Language: English
Topic: Finite Group Theory Research
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4407319856