Local density functional electronic structures of four isomers of C60H36, which have been proposed in the literature, are studied at geometries given by an empirical potential The conjugation of the unsaturated bonds is quite different in each structure, yet the ionization potentials of each are the same within 0.12 eV. There is even greater agreement among the electron affinities, which are negative. The tetrahedral isomer with four six-membered rings of unsaturated carbon atoms is energetically the most stable.