Über Wirkungsbereichsteilungen von kubischer Symmetrie *

Abstract

Abstract. Partitions of the three-dimensional space by Dirichlet domains with cubic symmetry have been studied and a method of their derivation is described. Detailed results are given for a section through a zone of high instability in the space group I4132-O8. 172 types of polyhedra could be found in this section and their three-dimensional fields of existence were determined. Two types of Dirichlet domains with 38 faces and 70 vertices were discovered. ct. Partitions of the three-dimensional space by Dirichlet domains with cubic symmetry have been studied and a method of their derivation is described. Detailed results are given for a section through a zone of high instability in the space group I4132-O8. 172 types of polyhedra could be found in this section and their three-dimensional fields of existence were determined. Two types of Dirichlet domains with 38 faces and 70 vertices were discovered.