A characterization of homothetic simplices
type: Item
instance of: scholarly article
title: A characterization of homothetic simplices
zbMATH Open document ID: 0952.52003
DOI: 10.1007/PL00009454
author: Valeriu Soltan
published in: Discrete \& Computational Geometry
publication date: 1999-10-26T00:00:00Z
review text: The author proves the following theorem: For convex bodies \(K_1, K_2\subset E^d,\) \(d\geq 1,\) the following conditions are equivalent: (1) \(K_1\) and \(K_2\) are homothetic \(d\)-simplices; (2) the \(d\)-dimensional intersections \(K_1\cap(z + K_2)\), \(z\in E^d,\) belong to a unique homothety class of convex bodies; (3) the \(d\)-dimensional intersections \(K_1\cap(z+ K_2)\), \(z\in E^d\), belong to at most countably many homothety classes of convex bodies.
Mathematics Subject Classification ID: 52A20
zbMATH DE Number: 1334937
zbMATH Keywords: convex bodies
zbMATH Keywords: homothetic simplices
zbMATH Keywords: intersections
zbMATH Keywords: homothety classes of convex bodies
zbMATH Keywords: Choquet simplex
zbMATH Keywords: homothety classes
zbMATH Keywords: characterization of homothetic simplices
reviewed by: Serguey M. Pokas
MaRDI profile type: Publication
full work available at URL: pl00009454
OpenAlex ID: W2072045427
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description: scientific article; zbMATH DE number 1334937