MNDO calculations are carried out on several fullerene structures relevant to recent tandem mass spectroscopic, photophysical studies. Estimates are presented for the enthalpy changes of Stone-Wales isomerization, of the excision of C2, C4, and C6 groups from buckminsterfullerene (BF), and of the excision of C2 from a closely related C62 molecule. The calculations support the general belief that the introduction of pentalene units into a fullerene is destabilizing. The removal of C2 from C62 to form BF is predicted to be strongly endothermic but not nearly to the same extent as the removal of C2 from BF itself. In the case of BF the calculations require the excision to be a multiphoton process, in agreement with reported interpretations of experimental data. Additional calculations indicate that C30 has at least one stable fullerene structure. This result is contrary to the photophysically based suggestion that C32 represents the lower limit of fullerene stability. The difficulty of forming reasonable geometric starting points for MNDO calculations is overcome by the use of inverse stereographic projection and the concept of a planar dual graph.