Fullerenes containing fused triples of pentagonal rings

Abstract

A geometrical construction is described that generates all fullerene isomers C _n 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 (D ₂ , D _2h , D _2d , T, T _d ). 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 D ₂ IPT fullerene without a spiral occurs at n=424. In the range of IPT fullerenes with up to 1000 atoms, D ₂ 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.