A numerical model is presented to determine the Keldysh adiabaticity parameter for the interaction of an intense laser with a polyatomic molecule. The adiabaticity parameter is a guide to determining whether the ionization process is in the field or multiphoton ionization regime. The adiabaticity parameters are compared for potentials including the simple zero-range potential, the Coulomb potential, an atomic potential (Xe), a diatomic (N-2) molecular potential, and a polyatomic (C6H6) molecular potential. It is demonstrated that the Coulomb potential is approximately equal to the atomic and diatomic potentials and differs from the zero-range potential employed in the Keldysh model in a way which is predominantly dependent upon the ionization potential. Both simple models substantially overestimate the adiabaticity parameter for C6H6 at all field strengths and at fields above 1.25 V/Angstrom both simple models become completely unphysical. This is because barrier suppression ionization is predicted to occur for benzene above 1.25 V/Angstrom using the ab initio potential. This field for barrier suppression ionization is significantly lower than the 1.5 V/Angstrom field predicted using the Coulomb model.