Zur Bestimmung asymmetrischer Einheiten kubischer Raumgruppen mit Hilfe von Wirkungsbereichen

Two different methods for the deduction of asymmetric units are proposed and have been applied to cubic space groups. Both these methods are based on the knowledge of the Dirichlet domains (Wirkungsbereiche) for special sets of equivalent points: (1) The Dirichlet domains for points in general positions directly give rise to asymmetric units. For the limiting cases, where higher symmetry is simulated by relations between the coordinates, these Dirichlet domains are known as those of special positions in supergroups. (2) According to point symmetry the Dirichlet domains for special positions may be split into asymmetric units for the space group under consideration. Selection of the simplest asymmetric unit for each space group leads to 15 different polyhedra for all cubic space groups. The part of the border of the asymmetric unit that belongs to the asymmetric unit is specified for each space group.