The highest-order axis of this chiral fullerene is the C3 axis passing through opposite and symmetry-equivalent six-membered rings (Fig. 10a). Numbering can begin in either one of these rings, the six atoms of which are symmetry-equivalent in two sets of three: a is equivalent to a' and a", and b is equivalent to b' and b". As a consequence there are four possible pathways to be considered: a to b to a'; a to b" to a"; b to a' to b'; b to a to b". The pathway b to a' to b' does not lead to a contiguous numbering, whereas the other three pathways do. These are reported in Figs. 10b (a to b to a'), 10c (a to b" to a"), and 10d (b to a to b"). Since all three pathways terminate at an atom belonging to the six-membered ring bisected by the reference axis, application of Fu-3.1.3 is inconclusive. Inspection of the atom sequences of Figs. 10b, 10c, and 10d according to Fu-3.1.4 (Table 4) shows that the sequence in Fig. 10d has a 6,6,5 atom at position 7, whereas those in Figs. 10b and 10c both have a 6,5,5 atom at the same position. The numbering of Fig. 10d is therefore preferred. CAS selects the same numbering [ref 3]. The stereodescriptor for the shown enantiomer of this inherently chiral fullerene is (f,sC) [ref 4].
Fig. 10. Systematic numbering of (f,sC)(C42-D3)[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