3.1.3. Systematic numbering for (C₇₈-C_2v)[5,6]fullerene

This fullerene contains a single C₂ axis which passes through the center of a six-membered ring on one side and the midpoint of a bond on the other side. According to Fu-3.1.2 the ring is preferred for beginning the numbering. Because of symmetry there are only three pathways to be considered, namely clockwise a to b to a', b to a' to a'', and a' to a'' to b' (Fig. 5a). These lead to the contiguous helical numberings shown in Fig. 5b, 5c, and 5d, respectively. By application of Fu-3.1.3 the numbering of Fig. 5c is preferred because it terminates at an atom belonging to the bond bisected by the C₂ axis, whereas the other numberings terminate at an atom one (Fig. 5d) and two (Fig. 5b) bonds removed from the C₂ axis, respectively.

Fig. 5. Systematic numbering of (C₇₈-C_2v)[5,6]fullerene

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