Existenzbedingungen homogener Kugelpackungen in Raumgruppen tetragonaler Symmetrie*

Abstract

The conditions for packing crystallographically equivalent spheres in three-dimensional space have been evaluated for the cases of tetragonal space groups. The concept of lattice complexes and the knowledge of subgroup relations have been used to facilitate the investigation. 1016 classes of symmetrically equivalent sphere packings have been found. These classes form 394 topologically defined types. Detailed results are given for space group P4/n as an example.