Chemical Applications of Topology and Group Theory. 20. Eight-Vertex Polyhedra and Their Rearrangements.
GEORGIA UNIV ATHENS DEPT OF CHEMISTRY
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There are 257 combinatorially distinct eight-vertex polyhedra, of which 14 are deltahedra. Of the 14 deltahedra only the bisdisphenoid, commonly known as the D2d or triangular dodecahedron, both lacks tetrahedral chambers and can be formed by the hybridization of only s,p, and d orbitals. Degenerate single and symmetrical parallel multiple diamond-square-diamond processes involving the 14 eight-vertex deltahedra are tabulated. Among the eleven such processes six single, two symmetrical double, one fully symmetrical triple, and two fully symmetrical quadruple those relating the bisdisphenoid to the 4,4-bicapped trigonal prim and square antiprism are of current chemical significance. Single, double, and quadrupole dsd rearrangements of the bidisphenoid are depicted as topologically equivalent cubes with added diagonals so that the pivot faces are faces of the underlying cube and the dsd processes involve shifting only the positions of selected diagonals without disturbing the 12 edges of the underlying cube. Keywords Isomers, Stereochemistry, Molecular structure, Isomerization, Molecular complexes.
- Atomic and Molecular Physics and Spectroscopy