Figure 13.

Part of a probable roads roadmap for fullerene structures, starting from some of the hex-Rings and leading to some of the fullerene cages permitted by the head-to-tail exclusion rule. Non-IPR hex-Rings and cages are above the dashed line; IPR hex-Rings and IPR cages are below it. IPR cages with N ≤ 84 are numbered among IPR cages according to Fowler and Manolopoulos (24); larger cages are numbered according to the order in which they are produced by CaGe. Bound carbon atoms or clathrin triskelia are lower in energy than free monomers, so the potential energy E of the system is lower for larger fullerene fragments or cages.