Dodecahedrane point group

Type 4. More than one axis higher than twofold point groups I d, /, , /, (also Th, T, 0,1). Methane (Td), cubane (Oh, Figure 1.1), dodecahedrane (//, Figure 1.1), and buckminsterfullerene, Cat (E, Chapter 11). The symbol Kh denotes the point group of the sphere. 

Counting the isomers arising by addition to, or substitution in, a basic framework is a mathematical problem with many practical applications in chemistry. In classical organic chemistry, for example, the number of derivatives of a compound was often cited as proof or disproof of structure. Point group theory that uses concepts familiar to most chemists and is easy to apply when the number of addends/substituents is small provides a unified method for deciding, for example, the number of dihydrides C70H2 of fullerene C70, or the number of trihalo-derivatives C2oHi7FClBr of dodecahedrane. All that is needed to determine such matters is the availability of the permutation character. Ter, of the atoms in the parent molecule. 

Since the dodecahedrane molecule has a geometry that overall is close to spherical, it seemed likely that it would pack into a crystal lattice with the individual molecules more or less completely disordered with respect to rotation about their centers of gravity. This proved not to be true. Rather it was originally concluded that the molecules are packed into the lattice with a maximally superimposed order between the point group and the space group. (It may be rananbered that fiiUeiene does have this rotational disorder (Chapter 5).) It was subsequently shown, however, that the experimental structure is the mean of three equivalent arrangements of lower symmetry. ... 

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