Periodica Mathematica Hungarica

, Volume 22, Issue 3, pp 139–146 | Cite as

Locally dense finite lattice packings of spheres

  • J. M. Wills


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.

The results support, to some extent, the hypothesis that real crystals grow preferably such that they need little volume, i.e that they are locally dense.

Mathematics subject classification numbers, 1980/1985

Primary 52A43 52A45 

Key words and phrases

Lattice packings 


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Copyright information

© Akadémiai Kiadó 1991

Authors and Affiliations

  • J. M. Wills
    • 1
  1. 1.Math. Inst.Univ. SiegenSiegenGermany

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