Some applications of a formula for the volume of a polyhedron
type: Item
instance of: scholarly article
title: Some applications of a formula for the volume of a polyhedron
zbMATH Open document ID: 1049.51007
published in: Siberian Advances in Mathematics
publication date: 2004-09-07T00:00:00Z
review text: Let \(P\) be a polyhedron in \(\mathbb R^3\) with triangular faces and given edge lengths. The author shows that for every `small' diagonal there is a polynomial equation, with coefficients depending only on the combinatorial structure, the edge lengths, and the volume of \(P\), such that the length of the diagonal is a root of this polynomial (a `small' diagonal is a diagonal between vertices of two faces with a common edge which do not belong to the edge and, of cause, are not joined by an edge). Some consequences of this fact are given. This is an English translation of the author's article published in the book [\textit{Yu. G. Reshetnyak} et al., Proceedings of the conference `Geometry and applications' dedicated to the 70th anniversary of Prof. Victor Toponogov. Novosibirsk: Izdatel'stvo Instituta Matematiki, 183--197 (2001; Zbl 0991.52005)].
Mathematics Subject Classification ID: 51M20
Mathematics Subject Classification ID: 51M25
Mathematics Subject Classification ID: 52C25
zbMATH DE Number: 2097412
zbMATH Keywords: polyhedra
zbMATH Keywords: polyhedral metric
zbMATH Keywords: volume
zbMATH Keywords: diagonal
zbMATH Keywords: polynomial equation
author: I. Kh Sabitov
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 2097412