3.2.2. Systematic numbering for (C₄₈-O_h)[4,6,8]fullerene

This fullerene, made up only of 8,6,4 atoms, posesses three symmetry-equivalent C₄ axes (Fig. 16a), four symmetry-equivalent C₃ axes (Fig. 16b), and six symmetry-equivalent C₂ axes (not shown: the axes pass through the midpoints of opposite four-membered rings). When one of the C₄ axes is used as the reference axis (Fig. 16a) and the pathway begins along a bond shared by a an eight- and a six-membered ring, the numbering becomes discontiguous at position 40. When, using the same axis, a bond shared by an eight- and a four-membered ring is selected to begin the numbering (namely, C-2 to C-3 in Fig. 16a), the discontiguity occurs at position 24. The numbering obtained using one of the C₃ axes as the reference axis and starting along a bond shared by an eight- and a six-membered ring is shown in Fig. 16b. In this case the discontiguity occurs at position 42. Using the same axis and starting along a bond shared by a six- and a four- membered ring (namely, C-2 to C-3 in Fig. 16b), the numbering becomes discontiguous at position 24. The use of a C₂ axis leads to numberings discontiguous at positions with lower locants. Therefore, on the basis of Fu-3.2.1a the numbering shown in Fig. 16b is preferred. According to Fu-3.2.4a, the numbering resumes at position 43 which is connected to 41, and then continues contiguously to position 48 according to Fu-3.2.4b.

Fig. 16. Systematic numbering of (C₂₄-O_h)[3,8]fullerene