Über Wirkungsbereichsteilungen von kubischer Symmetrie II. Die Typen von Wirkungsbereichspolyedern in den symmorphen kubischen Raumgruppen

Abstract

AbstractPartitions of the three-dimensional space by Dirichlet domains with cubic symmetry have been studied. Within the symmorphic cubic space groups a total of 91 different types of Dirichlet domains were found and their fields of existence were accurately determined. The occurence of the same type of Dirichlet domain in various space groups was investigated. In these space groups theP- undF-lattices exhibit very simple partitions with few different types of Dirichlet domains only, whereas in theI-lattices more complicated partitions occur.