3.2.6. Systematic numbering for (C₇₀-C_2v)[5,6]fullerene

This fullerene contains a single C₂ axis connecting the center of a six-membered ring at the near end and the midpoint of a bond at the far end, as shown in Fig. 20a. For symmetry reasons, three pathways must be considered in the ring: a to b to a"; a to a' to b'; and b to a to a'. They lead to numberings that become discontiguous at positions 54, 55, and 59, respectively (not shown). The only pathway that starts from the bond [(z to z') is equivalent to (z' to z), Fig. 20a] leads to the numbering shown in Fig. 20b; since this becomes discontiguous only at position 63 it is preferred on the basis of Fu-3.2.1a. The completion of the numbering represents an interesting example of the application of Fu-3.2.4 (see arrows in Fig. 20b). From position 63 a discontiguous step leads to atom 64 which is bound to atom 62 (Fu-3.2.4a). Moving on from atom 64 there are two possibilities, but the one going to the atom connected to atom 44 is preferred by Fu-3.2.4b. Atom 66 is selected again on the basis of Fu-3.2.4a, and Fu-3.2.4b allows the numbering to reach atoms 67 and 68. A final application of Fu-3.2.4 allows the last segment of the numbering to be completed.

Fig. 20. Systematic numbering of (C₇₀-C_2v)[5,6]fullerene