In this fullerene the plane of symmetry, orthogonal to the plane of the paper in Fig. 26, bisects five six-membered rings and two five-membered rings. The six-membered rings are preferred for beginning the numbering (Fu-184.108.40.206); they are indicated as A, B, C, D, and E in Fig. 26a (smaller-font letters denote rings away from the viewer; larger-font, bold letters denote rings closer to the viewer). Ring A contains only 6,6,5 atoms; rings B, C, and D contain two 6,6,6 and four 6,6,5 atoms, each; ring E contains four 6,6,6 and two 6,6,5 atoms. Therefore, ring E is preferred (Fu-220.127.116.11). The six atoms of ring E form three pairs of symmetry-equivalent atoms indicated as a/a', b/b', and c/c' in Fig. 26b. Because of symmetry only the six anticlockwise (or clockwise) pathways from each atom must be considered. They all lead to contiguous numbering. However, those starting from atoms b, b', c, and c' are preferred because they begin closer (0.5 bond) to the reference plane (<>Fu-3.3.3a). Two of these numberings (Figs. 26c and 26d) are preferred because they terminate at an atom 1.5 bonds removed from the reference plane (indicated by a bold dot), whereas the other terminates at an atom 2.5 bonds away from the plane (Fu-3.3.3b). Inspection of the atom ranking in the two preferred sequences reveals that the numbering in Fig. 26c is the correct numbering pathway because it begins with a 6,6,6 atom, whereas that in Fig. 26d begins with a 6,6,5 atom.
Fig. 26. Systematic numbering of (C54-Cs)[5,6]fullerene