Fig. 15. Systematic numbering of (C24-Oh)[3,8]fullerene
This fullerene, made up only of 8,8,3 atoms, possesses three symmetry-equivalent C4 axes (Fig. 15a), four symmetry-equivalent C3 axes (Fig. 15c), and six symmetry-equivalent C2 axes (these axes join midpoints of opposite 8,8 bonds). When one of the C4 axes is used as the reference axis, a contiguous pathway cannot be found starting along the bond shared by two eight-membered rings. In this case (Fig. 15a) the numbering becomes discontiguous at position 14. The numbering in Fig. 15b, obtained again using one of the C4 axes but starting along the bond shared by an eight- and a three-membered ring also becomes discontiguous at position 14. In Fig. 15c the numbering obtained using one of the C3 axes as the reference axis is shown. In this case, numbering becomes discontiguous at position 18. The numbering obtained using a C2 axis as the reference axis becomes discontiguous at a position with a locant lower than both 14 and 18. According to Fu-3.2.1a the numbering in Fig. 15c is preferred because the discontiguity occurs at a higher locant. According to Fu-3.2.4a, the numbering proceeds to position 19, which is connected to the numbered atom with the highest locant within reach (17). Within the second segment, numbering proceeds by the shortest path to position 22 which is connected to the the numbered atom with the lowest locant within reach (6) (Fu-3.2.4b). After another discontiguity, a third segment starts at position 23 (connected to atom number 21 according to Fu-3.2.4a) and ends with the last unnumbered, neighboring atom (24).
Fig. 15. Systematic numbering of (C24-Oh)[3,8]fullerene