Concordant Treatment of Various Skeletons having the Point Group Oh

Abstract

To differentiate between various Oh skeletons (octahedron, cube, cuboctahedron, truncated octahedron, and truncated hexahedron), the newly-developed combined-permutation representations are used under the GAP system, where their mark tables and USCI-CF tables are calculated. Because these tables are diferent from each other, they are standardized by using the newly-developed GAP functions to generate the standard mark table and the standard USCI-CF table. Thereby symmetry-itemized enumeration based on these Oh skeletons are conducted by applying Fujita's USCI approach (S. Fujita, Symmetry and Combinatorial Enumeration in Chemistry, Springer-Verlag, Berlin-Heidelberg, 1991).