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The basic definitions connected with sphere packings are given. The way in which sphere packings with tetragonal symmetry have been derived and assigned to generation classes and (topological) types is described. The results for tetragonal lattice complexes with zero and one degree of freedom are listed and – in the latter case – the sphere-packing conditions are illustrated by diagrams.

Tetragonal sphere packings: I. Lattice complexes with zero or one degree of freedom