Hexagonal and trigonal sphere packings. I. Invariant and univariant lattice complexes

All homogeneous sphere packings and all interpenetrating sphere packings have been derived that refer to the seven invariant and the 23 univariant lattice complexes belonging to the hexagonal crystal family. The respective sphere packings may be assigned to 66 types. In addition, one case of interpenetrating sphere packings was found. For five types, the inherent symmetry of some sphere packings with specialized metrical and coordinate parameters may become cubic. For two further types, namely 8/4/c1 (body-centered cubic lattice) and 12/3/c1 (face-centered cubic lattice), the inherent symmetry is cubic for all corresponding sphere packings. By means of a large number of examples, the applicability of sphere packings for the comparison and description of simple crystal structures is demonstrated.