Buckminsterfullerene point group

Key words Point groups, space groups, molecular symmetry, buckminsterfullerene, Jahn-Teller effect, chirality, dissymmetry, molecular packing, quasicrystals... 

In another nomenclature recommendation it was suggested that fullerenes be named in the same way as annulenes, for which the number of C-atoms is indicated in square brackets in front of the word [4]. For fullerenes the number of C-atoms is accompanied by the point group symmetry and by the number of the isomer (using capital Roman) in cases were there are more than one. This is especially important for higher fullerenes. Thus, for Buckminsterfullerene the full description is... 

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. 

Bromonimn ion, 108 N-Bromosuccinimide, 262 Brucine, in asymmetric synthesis, 10, 11 Buckminsterfullerene (Cgo) point group of, 6 Bullvalene, 170, 171 point group of, 4 Butadiene... 

Molecules with icosahedral symmetry are not new but the discovery of the newest of them, C6o or buckminsterfullerene, has had such a profound effect on chemistry in recent years that I thought it useful to include a discussion of the icosahedral point group to which C60 belongs. 

The symmetry of many molecules and especially of crystals is immediately obvious. Benzene has a six-fold symmetry axis and is planar, buckminsterfullerene (or just fullerene or footballene) contains 60 carbon atoms, regularly arranged in six- and five-membered rings with the same symmetry (point group //,) as that of the Platonic bodies pentagon dodecahedron and icosahedron (Fig. 2.7-1). Most crystals exhibit macroscopically visible symmetry axes and planes. In order to utilize the symmetry of molecules and crystals for vibrational spectroscopy, the symmetry properties have to be defined conveniently. 

Figure 2.7-1 Three objects belonging to the same point group //, the pentagondodecahedron, the icosahedron, and the buckminsterfullerene.

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