This chiral fullerene has three C2 axes, each intersecting the midpoint of a bond. These axes are indicated in Figs. 8a, 8b, and 8c. Application of Fu-188.8.131.52 allows to discard the axis in Fig. 8b because it bisects bonds connecting only 6,6,5 atoms, whereas in the other cases the corresponding bonds connect 6,6,6 atoms. The two bonds at the end of each reference axis in Figs. 8a and 8c are symmetry-equivalent, and only the inspection of the pathways originating from the atoms of one of these bonds is necessary. For symmetry reasons, there are two possible beginnings for the numbering in each Fig. 8a and Fig. 8c. These have been indicated as a to a' to b, and a to a' to c in each of these figures. Thus, there are four pathways to be considered. All of them are contiguous. The a to a' to b numbering in Fig. 8c terminates at an atom one bond removed from the bond bisected by the reference axis; the a to a' to c numbering in Fig. 8c terminates at an atom two bonds removed from the bond bisected by the axis; the two numberings in Fig. 8a terminate at atoms belonging to the bond bisected by the axis. According to Fu-3.1.3, the latter two numberings, shown in Figs. 8d and 8e, are preferred pathways, but a selection must still be made between them. Inspection of the ranking of the atoms according to rule Fu-3.1.4 (Table 2) shows that the atom at position 3 of Fig. 8d is a 6,6,5 atom whereas the atom at the same position in Fig. 8e is a 6,6,6 atom. Therefore the numbering of Fig. 8e is preferred for the shown structure. In this case the numbering is the same as that selected by CAS [ref 3]. The stereodescriptor for the shown enantiomer of this inherently chiral fullerene is (f,sC) [ref 4].
Fig. 8. Systematic numbering of (f,sC)(C76-D2)[5,6]fullerene
References for this section
3. A.L. Goodson, C.L. Gladys and D.E. Worst, J. Chem. Inf. Comp. Sci. 1995, 35, 969-978.
4. International Union of Pure and Applied Chemistry, Division of Organic Chemistry, Commission on Nomenclature of Organic Chemistry. "Nomenclature for the (C60-Ih) and (C70-D5h(6))[5,6]fullerenes (IUPAC recommendations 2002)", Pure Appl. Chem. 2002, 74, 629-695.
5. P.W. Fowler and D.E. Manolopoulos, An Atlas of Fullerenes, Clarendon Press, Oxford, 1995