More about the 52 four-dimensional parallelotopes
type: Item
instance of: scholarly article
title: More about the 52 four-dimensional parallelotopes
zbMATH Open document ID: 1155.52013
published in: Taiwanese Journal of Mathematics
publication date: 2008-09-29T00:00:00Z
review text: A parallelotope (in the sense of tilings) is a convex polytope filling the space by its translative copies without overlapping, i.e., a translative space-filler. The authors investigate the 52 types of four-dimensional parallelotopes. More precisely, they prove that there are exactly 17 four-dimensional unimodular vector systems, which yield precisely 17 types of zonotopal 4-parallelotopes. In addition it is shown that the remaining 35 types are: Schläfli's 24-cell, and 34 sums of the 24-cell and zonotopal parallelotopes. The constructions of these 34 types are described in detail.
reviewed by: Horst Martini
Mathematics Subject Classification ID: 52C22
Mathematics Subject Classification ID: 51M20
Mathematics Subject Classification ID: 52B15
zbMATH DE Number: 5348116
zbMATH Keywords: tiling
zbMATH Keywords: parallelotope
zbMATH Keywords: translative space-filler
zbMATH Keywords: 24-cell
zbMATH Keywords: zonotope
zbMATH Keywords: Voronoi polytope
zbMATH Keywords: Minkowski sum
zbMATH Keywords: permutohedron
author: Michel Deza
author: Viacheslav Grishukhin
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.11650/twjm/1500404985
OpenAlex ID: W1854774644
DOI: 10.11650/TWJM/1500404985
description: scientific article; zbMATH DE number 5348116