Pages 224-241 Citation of the article: S. Fujita and N. Matsubara, Edge Configurations on a Regular Octahedron. Their Exhaustive Enumeration and Examination With Respect to Edge Numbers and Point-Group Symmetries

Abstract

Abstract Motivation. The versatility of the USCI (unit-subduced-cycle-index) approach is demonstrated in characterizing the symmetries of octahedral complexes. Method. Edge configurations on a regular octahedron have been combinatorially enumerated by the PCI (partial-cycle-index) method, which is one of the four methods of the USCI approach. Results. Thereby, the complete set of edge configurations has been obtained, where all edge configurations are classified by virtue of two criteria, i.e., the numbers of edges and the point-group symmetries. The latter criterion enables us to examine chiral and achiral edge configurations, where complementary configurations are discussed in terms of the subductions of coset representations. Conclusions. The USCI approach provides a common tool to systematize inorganic stereochemistry as well as organic stereochemistry