In 2000, Andreas Hirsch and coworkers in Erlangen, Germany, formulated a rule to determine when a fullerene would be aromatic. They found that if there were 2(n + 1) π-electrons, then the fullerene would display aromatic properties. This follows from the fact that an aromatic fullerene must have full icosahedral (or other appropriate) symmetry, so the molecular orbitals must be entirely filled. This is possible only if there are exactly 2(n + 1) electrons, where n is a nonnegative integer. In particular, for example, buckminsterfullerene, with 60 π-electrons, is non-aromatic, since 60 ÷ 2 = 30, which is not a perfect square.
In 2011, Jordi Poater and Miquel Solà expanded the rule to determine when a fullerene species would be aromatic. They found that if there were 2n + 2n + 1 π-electrons, then the fullerene would display aromatic properties. This follows from the fact that a spherical species having a same-spin half-filled last energy level with the whole inner levels being fully filled is also aromatic.