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DOI: 10.1039/A701271C (Paper) Reference Section for: J. Chem. Soc., Faraday Trans., 1997, 93, 2255-2262

Fullerenes containing fused triples of pentagonal rings

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P. W. Fowler and J. E. Cremona

Abstract

A geometrical construction is described that generates all fullerene isomers Cn in which the twelve pentagonal faces are arranged in four separate fully fused triples. When such an isolated-pentagon-triple (IPT) fullerene achieves its maximal symmetry, it may belong to one of only five point groups (D2, D2h, D2d, T, Td). At large n, the class of IPT fullerenes includes some (chiral) isomers without face spirals. A systematic search shows that although the smallest unspirallable IPT fullerenes are tetrahedral (n=380, 404, T symmetry), high symmetry is not a prerequisite: the first D2 IPT fullerene without a spiral occurs at n=424. In the range of IPT fullerenes with up to 1000 atoms, D2 outnumber T counter-examples to the spiral conjecture by a factor of more than 10, but unspirallable fullerenes remain only a few percent of the IPT class as a whole.

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