Moving pentagons on nanocones

Abstract

Fullerenes are made by the intersection of twelve pentagonal nanocones. This note deals with an innovative isomeric mechanism, based on a sequence of Stone-Wales rotations, for moving the pentagonal face on the cusp of the nanocone. The modified nanocone is the seed for creating new fullerenes with different symmetry and size. Present results may help to model fullerene formation and, on the pure algorithmic side, may contribute to evolve the computer tools that generate fullerenes. This mechanism may also find application in mimicking the behaviors of biological systems that, like many viruses, are also describable in terms of spherical cages tiled by polygons.