Dihedral angles of convex polyhedra
type: Item
instance of: scholarly article
title: Dihedral angles of convex polyhedra
zbMATH Open document ID: 0951.52006
DOI: 10.1007/PL00009509
published in: Discrete \& Computational Geometry
publication date: 2000-12-13T00:00:00Z
review text: Let \(P\) be a compact convex polyhedron in hyperbolic 3-space \(H^3.\) It is classical to ask: Is \(P\) determined, among convex polyhedra, by its combinatorics and its dihedral angles? The author shows that some similar or related questions have negative answers. There exist pairs of non-congruent convex space-like polyhedra in the de Sitter space \(S_1^3\) with the same edge lengths or with the same dihedral angles. The same holds for convex polyhedra in \(S^3\subset\mathbb R^4.\) The examples are built from a well-known one-parameter family of polyhedra in \(\mathbb R^3\) with the same edge lengths, through a transformation discovered by Pogorelov for \(H^3\) and \(S^3.\)
Mathematics Subject Classification ID: 52B05
zbMATH DE Number: 1436022
zbMATH Keywords: compact convex polyhedron
zbMATH Keywords: de Sitter space \(S_1^3\)
zbMATH Keywords: combinatorics
zbMATH Keywords: dihedral angles
zbMATH Keywords: edge lengths
zbMATH Keywords: non-congruence
zbMATH Keywords: infinitesimal deformation
author: Jean-Marc Schlenker
reviewed by: Serguey M. Pokas
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1436022