Locally dense finite lattice packings of spheres

J. M. Wills

doi:10.1007/bf01960503

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Periodica Mathematica Hungarica

Volume/Issue:: Volume 22: Issue 3

Locally dense finite lattice packings of spheres

Author:

J. M. Wills

J. M. Wills Math. Inst. Univ. Siegen Hölderlinstr. 3 D-5900 Siegen Germany

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Pages:: 139–146

Online Publication Date:: 02 Aug 2005

Publication Date:: 01 Jun 1991

Article Category:: Research Article

DOI:: https://doi.org/10.1007/bf01960503

Keywords:: Primary 52A43; 52A45

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We consider finite packings of unit-balls in Euclidean 3-spaceE³ where the centres of the balls are the lattice points of a lattice polyhedronP of a given latticeL³⊃E³. In particular we show that the facets ofP induced by densest sublattices ofL³ are not too close to the next parallel layers of centres of balls. We further show that the Dirichlet-Voronoi-cells are comparatively small in this direction. The paper was stimulated by the fact that real crystals in general grow slowly in the directions normal to these dense facets.

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Periodica Mathematica Hungarica

Print ISSN:: 0031-5303

Online ISSN:: 1588-2829

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Periodica Mathematica Hungarica
Language	English
Size	B5
Year of Foundation	1971
Volumes per Year	2
Issues per Year	4
Founder	Bolyai János Matematikai Társulat - János Bolyai Mathematical Society
Founder's Address	H-1055 Budapest, Hungary Falk Miksa u. 12.I/4.
Publisher	Akadémiai Kiadó Springer Nature Switzerland AG
Publisher's Address	H-1117 Budapest, Hungary 1516 Budapest, PO Box 245. CH-6330 Cham, Switzerland Gewerbestrasse 11.
Responsible Publisher	Chief Executive Officer, Akadémiai Kiadó
ISSN	0031-5303 (Print)
ISSN	1588-2829 (Online)