A combination of topological and quantum mechanical techniques is used to predict the energetically favored isomer set for the experimentally detected but as yet uncharacterized C-116 fullerene. A systematic search and calculation at the QCFF/PI (quantum-consistent force field/pi) semiempirical level of the energies of the 6063 isomers of C-116 that satisfy the isolated-pentagon rule (IPR) find that the isomers in the most stable group have low degrees of eccentricity and are predicted by the highly discriminating hexagon-neighbor rule (HNR), for which a more generally applicable formulation is proposed.