Most favorable polyhedron

AVE parameter shifting the energy of MFP most favorable polyhedron... 

Three parameters are necessary to characterize the dodecahedron with triangular faces (see Fig. 6b). Hoard and Silverton chose for these parameters 0a, the angle between the M—A bond vector and the 4 axis of the polyhedron 0b, the corresponding angle made with the M—B bond vector and the ratio of the bond lengths, M—A vector/M—B vector. The most favorable values for these parameters are 0a = 35.2°, 0B == 73.5° and M—A/M—B = 1.03. The corresponding values for the hard sphere model are M—A = M—B, 0a = 36.9° and 0b = 69.5°. 

The most simple molecular topology of such systems reported so far is a tetrahedral supermolecule obtained by reacting tetrakis(dimethylsiloxy)-silane with alkenyloxy-cyanobiphenyls (Fig. 22), as discussed previously. Such tetramers exhibit smectic A liquid crystal phases [179]. For such end-on materials, microsegregation at the molecular level favors the formation of the smectic A phases in preference to the nematic phase exhibited by the mesogenic monomers themselves. The use of different polyhedral silox-ane systems (Fig. 24) or the Ceo polyhedron as the template for multi- and polypedal hexakis(methano)fullerenes (Fig. 70) substituted with a large number of terminally attached mesogenic groups confirm the same tendency to the formation of smectic A phases (vide supra). 

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