On edge-antipodal \(d\)-polytopes
type: Item
instance of: scholarly article
title: On edge-antipodal \(d\)-polytopes
zbMATH Open document ID: 1199.52026
author: T. Bisztriczky
author: Károly jun. Böröczky
published in: Periodica Mathematica Hungarica
publication date: 2009-12-28T00:00:00Z
review text: A convex \(d\)-polytope \(P\) is called edge-antipodal if any two vertices that determine an edge of \(P\) lie in different parallel supporting hyperplanes of \(P\). The authors introduce some ``program'' to investigate this type of polytopes, and they prove (among others) the following results on simple edge-antipodal polytopes: Simple edge-antipodal polytopes are antipodal in the usual sense, and there is a natural way to investigate arbitrary edge-antipodal polytopes to get a complete classification. Some nice characterizations of affine cubes are obtained, too.
reviewed by: Horst Martini
Mathematics Subject Classification ID: 52B11
Mathematics Subject Classification ID: 52B12
zbMATH DE Number: 5651840
zbMATH Keywords: convex
zbMATH Keywords: polytope
zbMATH Keywords: edge-antipodal
zbMATH Keywords: antipodality
zbMATH Keywords: cubical polytope
zbMATH Keywords: simple polytope
zbMATH Keywords: simplicial polytope
zbMATH Keywords: prism
MaRDI profile type: Publication
full work available at URL: s10998-008-8131-5
OpenAlex ID: W2044449173
cites work: Q5490264
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cites work: Q3446201
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DOI: 10.1007/S10998-008-8131-5
description: scientific article; zbMATH DE number 5651840