3.2.4. Systematic numbering for (C₃₄-C_2v)[4,6]fullerene

This fullerene contains one C₂ axis intersecting the midpoint of a six-membered ring at the near end and of a 6,6 bond at the far end (Fig. 18a). The six atoms of the ring form two sets of symmetry-equivalent atoms: a/a' and b/b'/b"/b'''. Three pathways must be considered: a to b to b'; b to b' to a'; and b to a to b". These lead to discontiguous numberings terminating at positions 20, 28 (Fig. 18b), and 25, respectively. The two atoms z and z' (Fig. 18a) connected by the bond at the far end of the axis are symmetry-equivalent. The pathway from z becomes discontiguous at position 32 (Fig 18c), and is therefore preferred on the basis of Fu-3.2.1a. The completion of this numbering according to Fu-3.2.4 is shown in Fig. 18c.

Fig. 18. Systematic numbering of (C₃₄-C_2v)[4,6]fullerene