Abstract
The packing density of large lattice packings of spheres in Euclidean E d measured by the parametric density depends on the parameter and on the shape of the convex hull P of the sphere centers; in particular on the isoperimetric coefficient of P and on the second term in the Ehrhart polynomial of the lattice polytope P. We show in E d , d ≥ 2, that flat or spherelike polytopes generate less dense packings, whereas polytopes with suitably chosen large facets generate dense packings. This indicates that large lattice packings in E 3 of high parametric density may be good models for real crystals.
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Wills, J.M. On Large Lattice Packings of Spheres. Geometriae Dedicata 65, 117–126 (1997). https://doi.org/10.1023/A:1004976720763
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DOI: https://doi.org/10.1023/A:1004976720763