A characterization of ideal polyhedra in hyperbolic 3-space
type: Item
instance of: scholarly article
title: A characterization of ideal polyhedra in hyperbolic 3-space
zbMATH Open document ID: 0874.52006
DOI: 10.2307/2118652
author: Igor Rivin
published in: Annals of Mathematics. Second Series
publication date: 1997-11-13T00:00:00Z
review text: This paper contains the sufficiency direction announced in the author's paper [Topology 32, No. 1, 87-92 (1993; Zbl 0784.52014)]. Two theorems characterize the dihedral angles of convex ideal polyhedra in \(H^3\), and also those ones where some vertices lie on the sphere at infinity and some in the finite part of \(H^3\). Author's dissertation, published in \textit{I. Rivin} and \textit{C. D. Hodgson} [Invent. Math. 111, No. 1, 77-111 (1993; Zbl 0784.52013); corr. ibid. 117, No. 2, 359 (1994; Zbl 0798.52009)], discusses also other remarkable results on the Steiner problem and E. M. Andreew's theorems. I repeat my suggestion: ``the author should write a monograph to elaborate his very remarkable results in full details''.
Mathematics Subject Classification ID: 52B10
Mathematics Subject Classification ID: 52A55
Mathematics Subject Classification ID: 51M10
zbMATH DE Number: 854848
zbMATH Keywords: hyperbolic 3-space
zbMATH Keywords: ideal polyhedra
reviewed by: Emil Molnár
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2307/2118652
OpenAlex ID: W2004902643
description: scientific article; zbMATH DE number 854848