Tessellations generated by hyperplanes
type: Item
instance of: scholarly article
title: Tessellations generated by hyperplanes
zbMATH Open document ID: 0613.52005
DOI: 10.1007/BF02187880
author: Rolf Schneider
published in: Discrete \& Computational Geometry
publication date: 1987-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/131019
review text: Let \({\mathcal H}\) be a locally finite system of hyperplanes in \({\mathbb{R}}^ d\) such that the cells of the induced cell complex decomposition \({\mathcal T}\) of \({\mathbb{R}}^ d\) have uniformly bounded diameters. If \({\mathcal H}\) is simple and the density of the vertices in \({\mathcal T}\) exists, then the density of the k-cells in \({\mathcal T}\) exists and further the mean number of j-faces of the k-cells in \({\mathcal T}\) exists. The author shows that these numbers are exactly those occurring from the cubical tesselation, generated by hyperplanes parallel to the coordinate hyperplanes. For certain nonsimple systems \({\mathcal H}\) corresponding inequalities are obtained.
Mathematics Subject Classification ID: 52A37
Mathematics Subject Classification ID: 52C17
Mathematics Subject Classification ID: 05B45
zbMATH DE Number: 3992331
zbMATH Keywords: tiling
zbMATH Keywords: convex cell
zbMATH Keywords: density
zbMATH Keywords: tesselation
reviewed by: Jörg M. Wills
MaRDI profile type: Publication
cites work: Q5547252
cites work: Q4777988
cites work: Facing up to arrangements: face-count formulas for partitions of space by hyperplanes
description: scientific article; zbMATH DE number 3992331