Volumes of complementary projections of convex polytopes
type: Item
instance of: scholarly article
title: Volumes of complementary projections of convex polytopes
zbMATH Open document ID: 0627.52005
DOI: 10.1007/BF01294650
author: Peter McMullen
published in: Monatshefte für Mathematik
publication date: 1987-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/178355
review text: It is shown that those centrally symmetric convex d-polytopes whose images under orthogonal projection on to any pair of orthogonal complementary subspaces of \({\mathbb{E}}^ d\) have numerically equal volumes are cartesian products of (centrally symmetric) polygons in \({\mathbb{E}}^ 2\) with the same property and unit line segments. For \(d\geq 3\), the general projection property in fact follows from that for pairs of hyperplanes and lines. A conjecture is made about the solution of the problem in the non-centrally symmetric case.
Mathematics Subject Classification ID: 52Bxx
zbMATH DE Number: 4019884
zbMATH Keywords: complementary orthogonal
zbMATH Keywords: centrally symmetric convex d-polytopes
zbMATH Keywords: orthogonal projection
zbMATH Keywords: volumes
MaRDI profile type: Publication
cites work: Q3756901
cites work: Q5547252
cites work: Q3317685
cites work: Q3036193
cites work: Combinatorial Properties of Associated Zonotopes
cites work: Lifting projections of convex polyhedra
cites work: Über die Projektionenkörper konvexer Polytope
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description: scientific article; zbMATH DE number 4019884