Combinatorial d-tori with a large symmetry group
type: Item
instance of: scholarly article
title: Combinatorial d-tori with a large symmetry group
zbMATH Open document ID: 0634.52008
DOI: 10.1007/BF02187905
published in: Discrete \& Computational Geometry
publication date: 1988-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/131044
review text: The zonotope which is the vector sum of the \(d+1\) segments joining the centroid of a regular d-simplex to its vertices tiles E d by translation. The authors show here that a suitable triangulation of it extends to a triangulation of E d, which under identification by certain translations yields a triangulation of the d-torus with \(n=2^{d+1}-1\) vertices and an automorphism group of order \(2(d+1)n\) acting transitively on the vertices. The case \(d=2\) is the well-known Czászár torus.
Mathematics Subject Classification ID: 52A37
zbMATH DE Number: 4032504
zbMATH Keywords: tiling
zbMATH Keywords: zonotope
zbMATH Keywords: triangulation
zbMATH Keywords: d-torus
zbMATH Keywords: automorphism group
author: Wolfgang Kühnel
author: Gunter Lassmann
MaRDI profile type: Publication
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cites work: Q5547252
cites work: Tilings with congruent tiles
cites work: Higherdimensional analogues of Császár's torus
cites work: The rhombidodecahedral tessellation of 3-space and a particular 15-vertex triangulation of the 3-dimensional torus
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cites work: Triangulations for the cube
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description: scientific article; zbMATH DE number 4032504