On large lattice packings of spheres
type: Item
instance of: scholarly article
title: On large lattice packings of spheres
zbMATH Open document ID: 0881.52012
DOI: 10.1023/A:1004976720763
published in: Geometriae Dedicata
publication date: 1997-04-27T00:00:00Z
review text: Let \(B^d\) denote the unit ball in \(E^d\), let \(L\) be a lattice such that \(L+B^d\) is a packing, let \(C_n\) be a set of \(n\) points in \(L\) and let \(P= \text{conv} C_n\). Then \(C_n+ B^d\) is a finite lattice packing with density \(nV(B^d)/V(P+ \rho B^d)\). The author shows that ``\(\dots\) flat or spherelike polytopes \(P\) generate less dense packings, whereas polytopes with suitably large facets generate dense packings. This indicates that large packings in \(E^3\) of high parametric density may be good models for real crystals''.
Mathematics Subject Classification ID: 52C17
Mathematics Subject Classification ID: 11H31
Mathematics Subject Classification ID: 05B40
zbMATH DE Number: 1003887
zbMATH Keywords: large lattice packings
zbMATH Keywords: spheres
author: Jörg M. Wills
MaRDI profile type: Publication
full work available at URL: a:1004976720763
OpenAlex ID: W1581054192
description: scientific article; zbMATH DE number 1003887