The mix of a regular polytope with a face
type: Item
instance of: scholarly article
title: The mix of a regular polytope with a face
zbMATH Open document ID: 1022.51018
published in: Annals of Combinatorics
publication date: 2003-03-25T00:00:00Z
review text: An abstract regular polytope is a certain kind of partially ordered set with a rank function and a flag transitive group of automorphisms. Classical examples arise from convex regular polytopes; in this case the automorphism groups are spherical Coxeter groups. Let \(P\) and \(Q\) be abstract regular polytopes with automorphism groups \(\Gamma(P)\) and \(\Gamma(Q)\), respectively. Then the mix of \(P\) and \(Q\) is a partially ordered set related to the product \(\Gamma(P)\times\Gamma(Q)\). The authors focus on the situation where \(Q\) is a face of \(P\). In particular, they prove that, for some cases, the mix of a polytope with one of its faces is again an abstract polytope. This does not hold in the general setting.
reviewed by: Michael Joswig
Mathematics Subject Classification ID: 51M20
zbMATH DE Number: 1887491
zbMATH Keywords: abstract regular polytopes
author: Peter McMullen
author: Egon Schulte
MaRDI profile type: Publication
full work available at URL: s00026-002-8032-1
OpenAlex ID: W2123783354
DOI: 10.1007/S00026-002-8032-1
description: scientific article; zbMATH DE number 1887491