Interpenetration of homogeneous sphere packings and of two-periodic layers of spheres

74 types of interpenetrating sphere packings and 4 types of interpenetrating layers of spheres exist that occur with highest symmetry in the cubic, hexagonal or tetragonal crystal family. The patterns of the interpenetration are analysed.

Hexagonal and trigonal sphere packings. IV. Trivariant lattice complexes of trigonal space groups

For the 13 trivariant lattice complexes of the trigonal space groups, all types of homogeneous sphere packings, interpenetrating sphere packings and layers are derived. Examples of related crystal structures are given.

Orthorhombic sphere packings. I. Invariant and univariant lattice complexes

All homogeneous sphere packings were derived that refer to the invariant and univariant lattice complexes with orthorhombic symmetry. Examples of corresponding crystal structures are given.