Periodic sphere packings and the Wulff-shape (Q1591722)

The asymptotic shape of large densest sphere packings in a lattice \(L\subset E^d\), \(d\geq 2\) is a polytope, the Wulff-shape, which in \(E^3\) models the shape of an ideal crystal in this special case. The density is measured by parametric density. The author shows that this also holds for the general case of periodic packings with spheres of different size. Although this case is much more general and more complicated, it still is a good model for the Wulff shape of crystals. This is underlined by 3 examples of different crystallographic type given in this paper. Besides these applications in 3-space the results hold for all \(d>3\).