Delaunay triangulation and triangulation of tori
type: Item
instance of: scholarly article
title: Delaunay triangulation and triangulation of tori
zbMATH Open document ID: 1187.57023
author: Alain Grigis
published in: Geometriae Dedicata
publication date: 2010-01-29T00:00:00Z
review text: Triangulations of the \(n\)-torus can be constructed from triangulations of the euclidean \(n\)-space which are invariant under a lattice. There is a standard triangulation which can be constructed from the cubical tessellation by triangulating each cube in the standard way. This was employed in the paper by the reviewer and \textit{G. Lassmann} in [Discrete Comput. Geom. 3, 169--176 (1988; Zbl 0634.52008)] for obtaining a triangulation of the \(n\)-torus with \(2^{n+1}- 1\) vertices. This is the minimum number so far obtained. For the 4-torus and the 8-torus the author constructed different triangulations with the same number of vertices. In the present paper the author starts from the Delaunay triangulation of a generic lattice in \(n\)-space. For the standard triangulation one can take the lattice \(A^*_n\). Each vertex link has \(2^{n+1}- 2\) vertices, thus suggesting the same minimum number of vertices as above.
Mathematics Subject Classification ID: 57Q15
Mathematics Subject Classification ID: 52C07
Mathematics Subject Classification ID: 52C22
zbMATH DE Number: 5664574
zbMATH Keywords: Voronoi cell
zbMATH Keywords: billiard
zbMATH Keywords: invariant triangulation
zbMATH Keywords: lattice triangulation
reviewed by: Wolfgang Kühnel
MaRDI profile type: Publication
full work available at URL: s10711-009-9374-1
OpenAlex ID: W2008750240
cites work: Q3941610
cites work: Q4049712
cites work: Q5566193
cites work: Q4039784
cites work: Separating maps of the lattice \(E_8\) and triangulations of the eight-dimensional torus
cites work: Triangulation of the 4-dimensional torus
cites work: The rhombidodecahedral tessellation of 3-space and a particular 15-vertex triangulation of the 3-dimensional torus
cites work: Combinatorial d-tori with a large symmetry group
cites work: Tiling the torus and other space forms
DOI: 10.1007/S10711-009-9374-1
description: scientific article; zbMATH DE number 5664574