A Pariser-Parr-Pople approach, complemented with physical consistency criteria based on the expected molecular response to a weak electric field, has been used to predict the electronic level structure and polarizabilities of five icosahedral fullerenes in the range C-60-C-720. The behavior of the polarizability alpha as a function of the fullerene size is given by the expression alpha =0.75R(e)(3), where R-e is an effective molecular radius. It is argued that fullerenes would present the maximum polarizability values allowed for carbon shells, as if they were made of graphene.