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Chemical Applications of Topology and Group Theory. 17. An Information Theoretical Approach to Polyhedral Symmetry.

ADA152821

Publication Date	1985
Personal Author	King, R. B.
Page Count	18
Abstract	Information theoretic parameters are described which measure the asymmetry of polyhedra based on partitions of their vertices, faces, and edges into orbits under action of their symmetry point groups. Such asymmetry parameters are all zero only for the five regular polyhedra and are all unity for polyhedra having no symmetry at all, i.e., belonging to the C sub 1 symmetry point group. In all other cases such asymmetry parameters have values between zero and unity. Values for such asymmetry parameters are given for all topologically distinct polyhedra having five, six, and seven vertices; all topologically distinct eight-vertex polyhedra having at least six symmetry elements; and selected polyhedra having from nine to twelve vertices. Effects on polyhedral distortions on these asymmetry parameters are examined for the tetrahedron, trigonal bipyramid, square pyramid, and octahedron. Such information theoretic asymmetry parameters can be used to order site partitions which are incomparable by the chirality algebra methods of Rush and co-workers.
Keywords	Isomerization Molecular complexes Measurement Stereochemistry Transformations Polygons Pyramids Ligands Edges Planar structures Asymmetry Topology Information theory Symmetry Polyhedra Vertices
Source Agency	Non Paid ADAS
NTIS Subject Category	99F - Physical & Theoretical Chemistry
Corporate Authors	Georgia Univ., Athens. Dept. of Chemistry.
Supplemental Notes	See also AD-A149 461.
Document Type	Technical Report
Title Note	Technical rept.
NTIS Issue Number	198515
Contract Number	N00014-84-K-0365

Chemical Applications of Topology and Group Theory. 17. An Information Theoretical Approach to Polyhedral Symmetry.

Chemical Applications of Topology and Group Theory. 17. An Information Theoretical Approach to Polyhedral Symmetry.
ADA152821

Publication Date	1985
Personal Author	King, R. B.
Page Count	18
Abstract	Information theoretic parameters are described which measure the asymmetry of polyhedra based on partitions of their vertices, faces, and edges into orbits under action of their symmetry point groups. Such asymmetry parameters are all zero only for the five regular polyhedra and are all unity for polyhedra having no symmetry at all, i.e., belonging to the C sub 1 symmetry point group. In all other cases such asymmetry parameters have values between zero and unity. Values for such asymmetry parameters are given for all topologically distinct polyhedra having five, six, and seven vertices; all topologically distinct eight-vertex polyhedra having at least six symmetry elements; and selected polyhedra having from nine to twelve vertices. Effects on polyhedral distortions on these asymmetry parameters are examined for the tetrahedron, trigonal bipyramid, square pyramid, and octahedron. Such information theoretic asymmetry parameters can be used to order site partitions which are incomparable by the chirality algebra methods of Rush and co-workers.
Keywords	Isomerization Molecular complexes Measurement Stereochemistry Transformations Polygons Pyramids Ligands Edges Planar structures Asymmetry Topology Information theory Symmetry Polyhedra Vertices
Source Agency	Non Paid ADAS
NTIS Subject Category	99F - Physical & Theoretical Chemistry
Corporate Authors	Georgia Univ., Athens. Dept. of Chemistry.
Supplemental Notes	See also AD-A149 461.
Document Type	Technical Report
Title Note	Technical rept.
NTIS Issue Number	198515
Contract Number	N00014-84-K-0365