3.4. Fullerenes belonging to the Ci or C1 point groups and having a contiguous helical numbering pathway.
In the achiral Ci fullerenes the center of inversion i is the only symmetry element. Different from the fullerenes examined so far, there are neither axes nor planes of symmetry passing through or lying upon a ring, a bond, or an atom, and the symmetry element, being inside the spheroid, cannot be used as a reference to begin the numbering. The chiral C1 fullerenes can be made identical to themselves only by a 360° rotation around any axis passing anywhere through the fullerene. Therefore, no axis can be used as a reference to begin the numbering since it does not have an unambiguously determined location.
For both Ci and C1 fullerenes, the absence of appropriate reference elements could lead to an undesirable increase of the number of possible numbering pathways. Therefore, the primary requirement of any numbering system should be the reduction of the allowed numbering options. Much in line with the procedure employed for the numbering of other fullerenes and in particular of Cs fullerenes, the following rules are adopted in order to decide where to begin the numbering.
Rule Fu-3.4.1. A larger ring is preferred to a smaller one to begin the numbering; among rings of the same size, the preferred ring contains the highest-ranking atom at the first point of difference.
Rule Fu-3.4.2. If there is still a choice among contiguous numberings, they are compared according to their atom-ranking sequence. The preferred pathway contains the highest-ranking atom at the first point of difference.
The numbering of Ci and C1 fullerenes proposed by CAS [ref 3] is also based on the identification of a preferred ring to begin the numbering. Incidentally, no example of numbering of Ci fullerenes has been reported by CAS.
3. A.L. Goodson, C.L. Gladys and D.E. Worst, J. Chem. Inf. Comp. Sci. 1995, 35, 969-978.