Contents
3.2. Fullerenes having at least one symmetry axis (Cn, n>1) but no contiguous helical pathway determined on the basis of rules Fu-3.1.1 to Fu-3.1.4
Fullerenes with at least one symmetry axis Cn, n>1 exist for which a contiguous helical pathway for numbering cannot be found using rules Fu-3.1.1 to Fu-3.1.4. The problem of numbering discountiguity in these fullerenes has already been tackled by previous publications [1,3], and solutions were proposed using different and sometimes non-clearly established procedures. To devise unique numbering for these fullerenes in a clear and relatively straightforward way, it was decided to establish a modified set of rules adopting an approach similar to that used in the case of fullerenes with contiguous numbering.
If no contiguous helical numbering can be found in a fullerene with at least one rotational axis of symmetry Cn, n>1 by application of rules Fu-3.1.1 to Fu-3.1.4, discontiguous numberings made up of two or more contiguous segments are examined, with the first of their segments being built around a proper rotation axis in complete analogy to the procedure employed in 3.1 to determine a contiguous pathway. If a preferred first segment is obtained based on rules Fu-3.2.1 to Fu-3.2.3 (see below), its follow-up segment(s) is (are) constructed based on rule Fu-3.2.4 (see below) to complete the preferred numbering. If there is still a choice after comparison of different first segments, subsequent segments are constructed (Fu-3.2.4) and compared (Fu-3.2.1 to Fu-3.2.3) at each level n until a preference becomes apparent.
Rule Fu-3.2.1 (cf. Fu-3.1.1):
Rule Fu-3.2.1
Rule Fu-3.2.2
Rule Fu-3.2.3
Rule Fu-3.2.4
3.2. Fullerenes having at least one symmetry axis (Cn, n>1) but no contiguous helical pathway determined on the basis of rules Fu-3.1.1 to Fu-3.1.4
Rule Fu-3.2.2 (cf. Fu-3.1.2): If there is a choice among reference axes of the same order or between the end of a reference axis to begin the numbering, Fu-3.1.2 is applied.
Rule Fu-3.2.3 (cf. Fu-3.1.4; for practical reasons, no rules analogous to Fu-3.1.3 is applied to segments of discontiguous numberings): When there is still a choice, the nth segments are compared according to rule Fu-3.1.4.
Once a preferred segment is identified based on rules Fu-3.2.1 to Fu-3.2.3 the numbering of the fullerene is completed by construction of the subsequent segment(s). The starting point of a new segment is defined according to rule Fu-3.2.4a (see below), and numbering within a segment is continued according to rule Fu-3.2.4b.
Rule Fu-3.2.4: After each discontiguity,