In this fullerene the plane of symmetry bisects three six-membered rings indicated as A, B, and C in Fig. 28a. Ring A contains the highest-ranking atom at the first point of difference than both rings B or C (ring A: four contiguous 6,6,5 atoms; rings B and C: two pairs of 6,6,5 atoms intercalated by single 6,5,5 atoms), and is therefore preferred to begin the numbering (Fu-184.108.40.206). However, none of the six possible pathways from A (clockwise and anticlockwise from a, b, and c) is contiguous. There are six pathways to be examined from ring B: from d and g (because these atoms are lying in the plane of symmetry it does not matter whether the numbering proceeds clockwise or anticlockwise), and clockwise and anticlockwise from e and f; and six from ring C: from h and k (because these atoms are lying in the plane of symmetry it does not matter whether the numbering proceeds clockwise or anticlockwise), and clockwise and anticlockwise from i and j. Of these only those from d, g, and the clockwise numbering from j are contiguous. They are shown in Figs. 28b, 28c, and 28d, respectively. Among these numberings, the one from j (Fig. 28d) is discarded because it begins out of the plane, whereas the others begin in the plane (Fu-3.3.3a). Application of rule Fu-3.3.3b does not help, since both numberings terminate at an atom 0.5 bond away from the plane. Eventually, a selection is made in favor of the numbering reported in Fig. 28c, because it features a 6,6,5 atom instead of a 6,5,5 atom at position 8 (Fu-3.3.4).
Fig. 28. Systematic numbering of (C50-Cs)[5,6]fullerene
5. P.W. Fowler and D.E. Manolopoulos, An Atlas of Fullerenes, Clarendon Press, Oxford, 1995