On neighborly families of convex bodies
type: Item
instance of: scholarly article
title: On neighborly families of convex bodies
zbMATH Open document ID: 1061.52002
author: A. V. Kuzminykh
published in: Journal of Geometry
publication date: 2004-09-22T00:00:00Z
review text: We say that a family of convex bodies in \(E^d\) is neighborly if the intersection of every two of them is \((d-1)\)-dimensional. The paper gives an answer to the question of \textit{B. Grünbaum} [Isr. J. Math. 1, 5--10 (1963; Zbl 0192.26604)] who asked how many members can a neighborly family of centrally symmetric convex bodies in \(E^d\) have? Namely, it is proved that for every \(d\geq 3\) there exists a sequence of neighborly centrally symmetric convex bodies which are pairwise affinely equivalent and which have prescribed volumes. What is more, those bodies have a large group of affine automorphisms. A similar fact is shown about neighborly families of similar polytopes whose diameters are prescribed.
reviewed by: Marek Lassak
Mathematics Subject Classification ID: 52A20
Mathematics Subject Classification ID: 52B11
Mathematics Subject Classification ID: 52B10
zbMATH DE Number: 2101782
zbMATH Keywords: convex body
zbMATH Keywords: centrally symmetric convex body
zbMATH Keywords: neighborly family
zbMATH Keywords: volume
MaRDI profile type: Publication
full work available at URL: s00022-003-1661-7
OpenAlex ID: W1970295104
DOI: 10.1007/S00022-003-1661-7
description: scientific article; zbMATH DE number 2101782