3.2.9. Systematic numbering for (C₈₄-D_2d)[5,6]fullerene

This fullerene contains three C₂ axes, each intersecting midpoints of opposite bonds as shown in Fig. 23a. Since the axes have the same order, the numbering can start at any of the bonds bisected by the axes. Only three pathways must be evaluated: a to a' to d; b to b' to e; c to c' to f. None of these leads to a contiguous numbering: all of them are discontiguous at position 81 (Fig. 23b, 23c, and 23d). Exploration of the numberings according to Fu-3.2.3 shows that the numberings reported in Fig. 23b and 23d are preferred because they contain a 6,6,6 atom at position 15. Further exploration shows that the numbering of Fig. 23b is preferred since it contains a 6,6,6 atom at position 19, whereas that of Fig. 23d contains a 6,6,5 atom at the same position. According to Fu-3.2.4, the completion of the numbering requires a discontiguous step to reach position 82 connected to the atom with the higher locant 80 (Fu-3.2.4a), a contiguous step to position 83 (Fu-3.2.4b), and a final discontiguous step to reach position 84.

Fig. 23. Systematic numbering of (C₈₄-D_2d)[5,6]fullerene

5. P.W. Fowler and D.E. Manolopoulos, An Atlas of Fullerenes, Clarendon Press, Oxford, 1995