Dihedral fullerenes of threefold symmetry with and without face spirals

Abstract

A general geometrical construction for fullerenes of threefold dihedral (D ₃ , D _3h , D _3d ) symmetry is reported and used to find those examples of this symmetry that are without face spirals. The smallest, a D ₃ 384-atom cage, has its twelve pentagons arranged in three separate crosses of four fully fused rings and has four atoms more than the smallest known non-spirallable fullerene. Another D ₃ structure, a 672-atom cage, is the smallest example of an isolated-pentagon fullerene without a spiral, improving on the previous upper bound by 128 atoms. Altogether, 61 new enantiomeric pairs of nonspirallable fullerenes with less than 1000 atoms belonging to four different classes, all of D ₃ symmetry, are identified.