Types of sphere packings for crystallographic point groups, rod groups and layer groups

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Abstract
All conceivable types of sphere packings for subperiodic crystallographic groups have been derived. To achieve this, it was possible to limit study to the characteristic classes of configuration-sets for the point complexes, row complexes and net complexes. The resulting 24 sphere-packing types of point groups, 60 sphere-packing types of rod groups and 75 sphere-packing types of layer groups are listed together with their generating symmetry operations. The sphere packings of point groups and rod groups can be classified uniquely by means of topological symbols. For this, modified Schläfli symbols have been used in the case of point groups. The sphere packings of rod groups can be described uniquely as plane nets rolled up according to a coincidence vector. Almost all sphere packings of layer groups may be assigned to plane nets or double nets, although a unique topological symbolism could not be developed in this case.

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