Arbitrarily large neighborly families of symmetric convex polytopes
type: Item
instance of: scholarly article
title: Arbitrarily large neighborly families of symmetric convex polytopes
zbMATH Open document ID: 0591.52007
DOI: 10.1007/BF00164398
author: Joseph Zaks
published in: Geometriae Dedicata
publication date: 1986-01-01T00:00:00Z
review text: A family of convex d-polytopes in \(E^ d\) is called neighborly if every two of them have a (d-l)-dimensional intersection. The purpose of this paper is to solve a problem of Grünbaum, showing that for every d, \(d\geq 3\), there exist arbitrarily large neighborly families of centrally symmetric convex d-polytopes in \(E^ d\), moreover, each member in such a family can be chosen to have a k-flat center of symmetry, for any k, \(0\leq k\leq d-1.\) In addition the author proves that for every \(d\geq 4\), m and t, \(0\leq t\leq d-1,\) there exists in \(E^ d\) a neighborly family of m congruent d-polytopes having a t-flat center of symmetry.
reviewed by: Károly Bezdek
Mathematics Subject Classification ID: 52Bxx
Mathematics Subject Classification ID: 52A20
Mathematics Subject Classification ID: 52C17
Mathematics Subject Classification ID: 52A37
zbMATH DE Number: 3949174
zbMATH Keywords: neighborly families of centrally symmetric convex d-polytopes in
zbMATH Keywords: \(E^ d\)
zbMATH Keywords: neighborly families of centrally symmetric convex d-polytopes in \(E^ d\)
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 3949174