On Coxeter's regular skew polyhedra
type: Item
instance of: scholarly article
title: On Coxeter's regular skew polyhedra
zbMATH Open document ID: 0597.52005
DOI: 10.1016/0012-365X(86)90017-8
published in: Discrete Mathematics
publication date: 1986-01-01T00:00:00Z
review text: The four regular skew polyhedra \(\{\) 4,6\(| 3\}\), \(\{\) 6,4\(| 3\}\), \(\{\) 4,8\(| 3\}\) and \(\{\) 8,4\(| 3\}\) in \({\mathbb{E}}^ 4\) were first considered by \textit{H. S. M. Coxeter} [Proc. Lond. Math. Soc., II. Ser. 43, 33-62 (1937; Zbl 0016.27101)]. The present authors describe symmetric embeddings of these polyhedra in \({\mathbb{E}}^ 3\), and also discuss their regularity.
Mathematics Subject Classification ID: 52Bxx
Mathematics Subject Classification ID: 51M20
zbMATH DE Number: 3962624
zbMATH Keywords: automorphism
zbMATH Keywords: polyhedral realization
zbMATH Keywords: regular skew polyhedra
zbMATH Keywords: symmetric embeddings
author: Egon Schulte
author: Jörg M. Wills
MaRDI profile type: Publication
cites work: Regular Skew Polyhedra in Three and Four Dimension, and their Topological Analogues
cites work: The Abstract Groups G m,n,p
cites work: Self-dual configurations and regular graphs
cites work: Q3275862
cites work: Q5566193
cites work: Q5672665
cites work: Q3908122
cites work: Regular and semi-regular polytopes. I
cites work: Q3855356
cites work: Reguläre Inzidenzkomplexe. I
cites work: A combinatorial theory of Gruenbaum's new regular polyhedra. I: Gruenbaum's new regular polyhedra and their automorphism group
cites work: Q5344632
cites work: Regular polyhedra - old and new
cites work: Q3852200
cites work: Equivelar polyhedral manifolds in \(E^ 3\).
cites work: A Polyhedral Realization of Felix Klein's Map {3, 7}8 on a Riemann Surface of Genus 3
cites work: Geometric realizations for Dyck's regular map on a surface of genus 3
cites work: Q3689009
cites work: Q3038089
full work available at URL: 0012-365x(86)90017-8
OpenAlex ID: W2006668438
description: scientific article; zbMATH DE number 3962624