3.2.10. Systematic numbering for (C₁₁₂-T_d)[5,6]fullerene

This fullerene features four symmetry-equivalent C₃ axes connecting the midpoint of a six-membered ring on one side and an atom at the intersection of three six-membered rings on the other side (Fig. 24a); and three symmetry-equivalent C₂ axes connecting the midpoints of opposite six-membered rings (Fig. 24b). For symmetry reasons, there are two pathways to be considered starting from the hexagon bisected by the C₃ axis: from a and from b. The former (shown in Fig. 24c) becomes discontiguous at position 111; the latter at position 93. The only pathway starting from the atom z (Fig. 24a) lying on the C₃ axis becomes discontiguous at position 72. Using one of the C₂ axes as the reference axis, three clockwise pathways must be considered: from c, from d', and from d (Fig. 24b). They lead to numberings becoming discontiguous at positions 74, 104, and 107, respectively. Therefore, the numbering in Fig. 24c is preferred according to Fu-3.2.1.

Fig. 24. Systematic numbering of (C₁₁₂-T_d)[5,6]fullerene