This fullerene contains a single C2 axis at the intersection of two mirror planes; the axis passes through the center of a six-membered ring on one side and the midpoint of a bond on the other side. According to Fu-3.1.2 the ring is preferred for beginning the numbering. Because of symmetry there are only three pathways to be considered, namely a to b to c, b to c to a', and c to a' to b' (Fig. 13a). The first pathway does not lead to a contiguous helical numbering. The other two (Figs. 13b and 13c) do. Both terminate at an atom belonging to the bond bisected by the reference axis, and application of Fu-3.1.3 is inconclusive. By inspection of the atom ranking according to Fu-3.1.4 the numbering of Fig. 13b is preferred because it begins with a 6,6,6 rather than with a 6,6,5 atom (Fig. 13c).
Fig. 13. Systematic numbering of (C78-C2v)[5,6]fullerene
Reference for this section
5. P.W. Fowler and D.E. Manolopoulos, An Atlas of Fullerenes, Clarendon Press, Oxford, 1995