Tetrahedra are not reduced
type: Item
instance of: scholarly article
title: Tetrahedra are not reduced
zbMATH Open document ID: 1018.52006
DOI: 10.1016/S0893-9659(02)00057-5
author: Horst Martini
author: Walter Wenzel
published in: Applied Mathematics Letters
publication date: 2003-03-10T00:00:00Z
review text: A convex body (i.e., a compact convex set with interior points in \(\mathbb R^n\), \(n\geq 2\)) which does not properly contain a convex body with the same minimal width is said to be reduced. It is known that every regular \(m\)-gon in \(\mathbb R^2\) with odd vertex number \(m\) is reduced. Being motivated by the problem `Do there exist reduced \(n\)-polytopes for \(n\geq 3\)?' posed by \textit{M. Lassak} in [T. Bisztriczky, P. McMullen, R. Schneider, and A. Weiss (eds.), Polytopes: abstract, convex and computational (Dordrecht: Kluwer Academic Publishers) (1994; Zbl 0797.00016)], the authors prove that there is no reduced (nondegenerate) tetrahedron in \(\mathbb R^3\). In the general case, Lassak's problem is still open.
Mathematics Subject Classification ID: 52B10
Mathematics Subject Classification ID: 52A15
Mathematics Subject Classification ID: 52A20
Mathematics Subject Classification ID: 52B11
zbMATH DE Number: 1878896
zbMATH Keywords: reduced body
zbMATH Keywords: complete set
zbMATH Keywords: convex body of constant width
zbMATH Keywords: equifacial tetrahedron
zbMATH Keywords: isosceles tetrahedron
reviewed by: Victor Alexandrov
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1878896