The Carbon Cylinder Rule

Properly closed shells are found for cylinders C with either hemi-Ceo or 

Closed-shell fullerenes following the carbon cylinder mle are again rare (just 3 for ft 100) and again an experimentally characterized fullerene is the parent of an infinite series of properly closed shells. For n 112 the leapfrog and cylinder rules together exhaust the list of properly closed shells. They are not complete for all n, however, as the next section points out. 

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A survey of the Hiickel spectra of the lower fullerenes rapidly reveals that properly closed n shells are very much the exception rather than the rule most fullerene isomers have pseudoclosed k configurations. The rare occurrences of properly closed shells can be almost entirely described by two magic number rules that are to the fullerenes what the Hiickel 4n + 2 is to monocyclic systems and the Wade n + 1 rule is to boranes. The two are the leapfrog and the carbon cylinder rules. 

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