The geometrical characteristics of the α-ThSi2 structure type and of its parameter field

The 2-dimensional parameter field for the α-ThSi2-structure type is discussed with respect to limiting complexes. Dirichlet partitions and sphere configurations. On this basis privileged arrangements of the thorium atoms and of the silicon atoms are derived and compared with the crystal structure of α-ThSi2. The unusual geometrical properties of the idealized α-ThSi2 structure are elucidated. The deviations of the structures of EuSi2, CaSi2, SrSi2 and BaGe2 from the idealized ones are discussed. (orig.)