Some infinite families of finite incidence-polytopes
type: Item
instance of: scholarly article
title: Some infinite families of finite incidence-polytopes
zbMATH Open document ID: 0705.51015
DOI: 10.1016/0097-3165(90)90047-Z
author: Asia Ivić Weiss
published in: Journal of Combinatorial Theory. Series A
publication date: 1990-01-01T00:00:00Z
review text: The author constructs infinite families of finite universal abstract regular polytopes, whose facets and vertex-figures are both regular maps whose types are specified by the lengths of their Petrie polygons. (The universality means that the facets and vertex-figures alone determine the polytopes.) These families are: \({}_ 4\{2n,4,3\}_ 6\), \({}_ 4\{4,2n,3\}_ 6\), \({}_ 4\{4,2n,4\}_ 4\), \({}_ 6\{3,2n,3\}_ 6\) and \({}_ 4\{3,3,2n\}_ 6\), for each \(n\geq 2\); the two suffixes refer to the Petrie polygons of the facet and vertex-figure, respectively.
Mathematics Subject Classification ID: 51M20
zbMATH DE Number: 4157375
zbMATH Keywords: Petrie polygon
zbMATH Keywords: universal abstract regular polytopes
zbMATH Keywords: facet
zbMATH Keywords: vertex- figure
MaRDI profile type: Publication
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full work available at URL: 0097-3165(90)90047-z
OpenAlex ID: W2070989625
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description: scientific article; zbMATH DE number 4157375