3.3.4. Systematic numbering for (C₈₂-C_s)[5,6]fullerene

In this fullerene the plane of symmetry bisects five six-membered rings indicated as A, B, C, D, and E in Fig. 30a. Ring C contains only 6,6,5 atoms; rings B and E contain two 6,6,6 and four 6,6,5 atoms, each; ring A contains four 6,6,6 and two 6,6,5 atoms; ring D contains only 6,6,6 atoms, and thus is preferred to begin the numbering (Fu-3.3.2.1). However, none of the pathways from this ring is contiguous, and the pathways from ring A, which contains a sequence of four 6,6,6 atoms must be examined. The atoms of this ring are indicated as a/a', b/b', and c/c' in Fig. 30a. There are six clockwise pathways to be examined, one from each atom. Only those from a (Fig. 30b) and from b' (Fig. 30c) are contiguous. The latter is preferred because it starts closer to the reference plane (Fu-3.3.3a).

Fig. 30. Systematic numbering of (C₇₀-C_s)[5,6]fullerene

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