Three-dimensional polytopes inscribed in and circumscribed about compact convex sets
type: Item
instance of: scholarly article
zbMATH Open document ID: 0988.52016
author: V. V. Makeev
publication date: 2002-07-22T00:00:00Z
Mathematics Subject Classification ID: 52B10
Mathematics Subject Classification ID: 52B15
zbMATH DE Number: 1637580
zbMATH Keywords: survey
zbMATH Keywords: three-dimensional polytopes
zbMATH Keywords: inscribed
zbMATH Keywords: circumscribed
zbMATH Keywords: constant width
zbMATH Keywords: centrally symmetric
zbMATH Keywords: parallelepiped
MaRDI profile type: Publication
title: Three-dimensional polytopes inscribed in and circumscribed about compact convex sets
published in: St. Petersburg Mathematical Journal
review text: This paper gives a survey of results on three-dimensional polytopes such their images under a similarity are inscribed in or circumscribed about a three-dimensional compact set. The cases of the tetrahedron, pentahedron, hexahedron and heptahedron are treated in detail. The rest of the paper concentrates on the problem of polyhedra circumscribed about compact convex sets of constant width, as well as on polyhedra inscribed in or circumscribed about a centrally symmetric compact convex set.NEWLINENEWLINENEWLINEIn this last part the author proves the new result that, if \(K\) is a centrally symmetric convex compact set, then either the boundary of \(K\) contains the midpoints of the edges of a rectangular parallelepiped, or a certain central section of \(K\) is a rectangle.
reviewed by: Charles Leytem
description: scientific article; zbMATH DE number 1637580