This fullerene contains only 6,6,4 atoms. A contiguous helical pathway cannot be obtained using the three equivalent C4 axes passing through opposite tetragonal faces (Fig. 4a). Therefore, following Fu-3.1.1, the four equivalent C3 axes passing through opposite symmetry- equivalent hexagons are examined (Fig. 4b). Only the clockwise or anticlockwise pathways (both are equivalent for this achiral fullerene) starting along one of the three symmetry- equivalent bonds connecting symmetry-equivalent atoms (a and a') lead to contiguous numberings. The clockwise numbering is shown in Fig. 4c. Pathways around the lower-order C2 axes do not need to be considered.
Fig. 4. Systematic numbering of (C24-Oh)[4,6]fullerene
4. International Union of Pure and Applied Chemistry, Division of Organic Chemistry, Commission on Nomenclature of Organic Chemistry. "Nomenclature for the (C60-Ih) and (C70-D5h(6))[5,6]fullerenes (IUPAC recommendations 2002)", Pure Appl. Chem. 2002, 74, 629-695.