Minimal simplicial dissections and triangulations of convex 3-polytopes
type: Item
instance of: scholarly article
title: Minimal simplicial dissections and triangulations of convex 3-polytopes
zbMATH Open document ID: 0966.52009
author: N. Delaunay
published in: Discrete \& Computational Geometry
publication date: 2001-01-04T00:00:00Z
review text: The authors prove here the following somewhat surprising results about convex 3-polytopes. Let \(P\) be such a polytope. First, it is possible that the minimum number of tetrahedra in a triangulation of \(P\) can be reduced if one permits interior vertices. Second, there may be dissections of \(P\) into tetrahedra which use fewer tetrahedra than any triangulation. Third, the number of tetrahedra in a minimal triangulation of \(P\) may depend on the geometrical realization of \(P\) (as a combinatorial type). The families of examples they produce exhibit increasing large discrepancies.
Mathematics Subject Classification ID: 52B10
zbMATH DE Number: 1495779
zbMATH Keywords: dissection
zbMATH Keywords: geometric realization
zbMATH Keywords: convex 3-polytopes
zbMATH Keywords: triangulation
reviewed by: Peter McMullen
MaRDI profile type: Publication
full work available at URL: s004540010058
OpenAlex ID: W1981943800
DOI: 10.1007/S004540010058
description: scientific article; zbMATH DE number 1495779