Arbitrarily large neighborly families of symmetric convex polytopes

Joseph Zaks

doi:10.1007/BF00164398

Arbitrarily large neighborly families of symmetric convex polytopes

Joseph Zaks

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

A family of convex d-polytopes in E_dis called neighborly if every two of them have a (d-1)-dimensional intersection. Settling an old problem of B. Grünbaum, we show that there exist arbitrarily large neighborly families of centrally (or any other prescribed type of) symmetric convex d-poliytopes in E_d,for all d≥3; moreover, they can all be congruent, if d≥4.

Original language	English
Pages (from-to)	175-179
Number of pages	5
Journal	Geometriae Dedicata
Volume	20
Issue number	2
DOIs	https://doi.org/10.1007/BF00164398
State	Published - Apr 1986

ASJC Scopus subject areas

Geometry and Topology

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10.1007/BF00164398

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abstract = "A family of convex d-polytopes in Edis called neighborly if every two of them have a (d-1)-dimensional intersection. Settling an old problem of B. Gr{\"u}nbaum, we show that there exist arbitrarily large neighborly families of centrally (or any other prescribed type of) symmetric convex d-poliytopes in Ed,for all d≥3; moreover, they can all be congruent, if d≥4.",

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Arbitrarily large neighborly families of symmetric convex polytopes

Abstract

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