3. Numbering of fullerenes other than (C₆₀-I_h)[5,6]- and (C₇₀-D_5h(6))[5,6]-fullerene

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3. Numbering of fullerenes other than (C₆₀-I_h)[5,6]- and (C₇₀-D_5h(6))[5,6]-fullerene
   Rule Fu-3.1.2.1
   Rule Fu-3.1.2.2
   Rule Fu-3.1.2.3
   Rule Fu-3.1.4
3.1. Fullerenes having at least one symmetry axis (C_n, n>1) and a contiguous helical numbering pathway determined on the basis of rules Fu-3.1.1 to Fu-3.1.4.

While rules Fu-3.1.1, Fu-3.1.2, and Fu-3.1.3 are sufficient to systematically number (C₆₀-I_h)[5,6]- and (C₇₀-D_5h(6))[5,6]-fullerene, the numbering of other fullerenes may require additional rules. Some of these rules have already been proposed [ref 4].

Rule Fu-3.1.2.1: When there is a choice between rings for the beginning of numbering, a larger ring is preferred to a smaller one. When there is still a choice, the preferred ring contains the highest ranking atom at the first point of difference. The highest ranking atom is defined as the common atom of the set of three largest rings. For example, in a [5,6]fullerene, an atom at the intersection of three six-membered rings (in short, a 6,6,6 atom) ranks higher than an atom at the intersection of two six-membered rings and a five-membered ring (a 6,6,5 atom).

Rule Fu-3.1.2.2: When there is a choice between bonds bisected by an axis for the beginning of numbering, the preferred bond contains the higher number of higher ranking atoms.

Rule Fu-3.1.2.3: When there is a choice between atoms lying on an axis for the beginning of numbering, the numbering must start at the higher ranking atom.

In addition to the recommendations of ref. 4 one new rule was adopted:

Rule Fu-3.1.4: When there is still a choice among helical pathways for numbering, they are evaluated by sequential comparison of the ranking of their atoms. The preferred pathway contains the highest ranking atom at the first point of difference.

Based on the rules required for the numbering of their atoms, fullerenes considered in this document are divided into the following classes:

3.1 Fullerenes having at least one symmetry axis (C_n, n>1) and a contiguous helical numbering pathway determined on the basis of rules Fu-3.1.1 to Fu-3.1.4.

3.2 Fullerenes having at least one symmetry axis (C_n, n>1) but no contiguous helical numbering pathway determined on the basis of rules Fu-3.1.1 to Fu-3.1.4.

3.3 Fullerenes belonging to the C_s point group and having a contiguous helical numbering pathway determined unambiguously as described under 3.3 below.

3.4 Fullerenes belonging to the C_i or C₁ point groups and having a contiguous helical numbering pathway determined unambiguously as described under 3.4 below.

There are fullerenes belonging to this class whose numbering can be devised solely on the basis of Fu-3.1.1 to Fu-3.1.4. Examples are given below.

• 3.1.1. (C₂₀-I_h)[5]fullerene
• 3.1.2. (C₂₄-O_h)[4,6]fullerene
• 3.1.3. (C₇₈-C_2v)[5,6]fullerene
• 3.1.4. (C₄₈-C₂)[5â6]fullerene

4. International Union of Pure and Applied Chemistry, Division of Organic Chemistry, Commission on Nomenclature of Organic Chemistry. "Nomenclature for the (C₆₀-I_h) and (C₇₀-D_5h(6))[5,6]fullerenes (IUPAC recommendations 2002)", Pure Appl. Chem. 2002, 74, 629-695.