A bound on the ratio between the packing and covering densities of a convex body
type: Item
instance of: scholarly article
title: A bound on the ratio between the packing and covering densities of a convex body
zbMATH Open document ID: 0952.52017
DOI: 10.1007/PL00009503
author: Yanyan Li
published in: Discrete \& Computational Geometry
publication date: 2001-01-03T00:00:00Z
review text: A convex body is a compact convex set having a nonempty interior. The author considers packings and coverings with centrally symmetric convex bodies. It is proved that for any such body, the ratio between the density of its thinnest lattice covering of Euclidean 3-space and the density of its tightest lattice packing in Euclidean 3-space is less than or equal to 4.
Mathematics Subject Classification ID: 52C17
Mathematics Subject Classification ID: 52C07
zbMATH DE Number: 1436016
zbMATH Keywords: convex body
zbMATH Keywords: density
zbMATH Keywords: Euclidean 3-space
zbMATH Keywords: lattice covering
zbMATH Keywords: lattice packing
reviewed by: Patric R. J. Östergård
MaRDI profile type: Publication
Recommended article: On a relation between packing and covering densities of convex bodies
Recommended article: An inequality linking packing and covering densities of plane convex bodies
Recommended article: On the lower bound of packing density for convex bodies in the plane
Recommended article: On the packing densities and the covering densities of the Cartesian products of convex bodies
Recommended article: Q3738167
Recommended article: Computing upper bounds for the packing density of congruent copies of a convex body
Recommended article: On packings and coverings of unit density
Recommended article: Inequalities between lattice packing and covering densities of centrally symmetric plane convex bodies
description: scientific article; zbMATH DE number 1436016