Ionpackings in the space (Q1086844)

In euclidean 3-space \(E^ 3\) a lattice-packing K of unit spheres is called an ionpacking (with parameter \(\sqrt{2})\), if the centers of K split into two classes such that for each class the centers in this class have distance at least \(2\sqrt{2}\). The author proves that the packing density of an ionpacking K in \(E^ 3\) is at most \(\pi\) /6, with equality if and only if K is given by a cubic lattice with edge length 2 and the two classes of alternate vertices of this lattice.