Locally projective regular polytopes
type: Item
instance of: scholarly article
title: Locally projective regular polytopes
zbMATH Open document ID: 0792.52005
DOI: 10.1016/0097-3165(94)90033-7
published in: Journal of Combinatorial Theory. Series A
publication date: 1994-07-28T00:00:00Z
review text: The 2-sections of a finite regular polytope are polygons, i.e., they are spherical. If all the sections are spheres, then the combinatorially regular polytopes are obtained, which are known to be isomorphic to the convex regular polytopes. A natural question is the following: what happens if the minimal sections are of some other (sufficiently simple) topological type? If these minimal sections are all that is needed to determine the polytope, then the polytope is universal of its type. So a regular polytope is said to be locally projective if its minimal sections which are not spherical are projective spaces, and if these sections which are not spherical are projective spaces, and if these sections (together with the Schläfli type) determine the polytope. For each \(n\geq 4\), a family of \(n\) or \(n-1\) (as \(n\) is odd or even) locally projective regular polytopes is described, and these polytopes are shown to be universal of their type.
reviewed by: Horst Martini
Mathematics Subject Classification ID: 52B15
Mathematics Subject Classification ID: 20F55
zbMATH DE Number: 529903
zbMATH Keywords: abstract regular polytopes
zbMATH Keywords: universal polytopes
zbMATH Keywords: symmetry group
zbMATH Keywords: combinatorially regular polytopes
zbMATH Keywords: minimal sections
zbMATH Keywords: locally projective regular polytopes
author: Peter McMullen
MaRDI profile type: Publication
full work available at URL: 0097-3165(94)90033-7
OpenAlex ID: W1988328510
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description: scientific article; zbMATH DE number 529903