Chemical Applications of Topology and Group Theory. 22. Lowest Degree Chirality Polynomials for Regular Polyhedra.
GEORGIA UNIV ATHENS
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The lowest degree chirality polynomials for the regular octahedron, cube, and regular icosahedron are discussed. All three of these regular polyhedra are chirally degenerate since they have more than one lowest degree chiral ligand partition by the Ruch-Schonhofer scheme. The two lowest degree chirality polynomials for the octahedron have degree 6 and can be formed from three degree 3 generating polynomials f, g, and h through the relationships fgh and fg-h where f, g, and h measure the effects of the three separating reflection planes delta sub h, the four threefold rotation axes, and the three fourfold rotation axes, respectively. The permutation groups of the vertices of the cube and icosahedron contain only even permutations which leads to a natural pairing of their chiral ligand partitions according to equivalence of the corresponding Young diagrams ulon reflection through their diagonals.
- Organic Chemistry
- Theoretical Mathematics