A theoretical investigation of fullerene, C-80 using density functional theory is presented. Following the isolated pentagon rule (IPR), seven different topologies are considered. Calculated energy differences are less than 30 kJ/mol except for I-h topology which is more unstable. Isomers of D-5d, C-2v(I), and D-2 topology are found to have singlet ground states. Calculated nuclear magnetic resonance and electronic absorption spectra allow to identify the two known isomers as D-2-and D-5d in agreement with previous assignments. The absolute configuration of the chiral D-2 isomer is predicted by means of the calculated electronic circular dichroism spectrum. The results further suggest that the C-2v(I) isomer might be accessible from soots. All other IPR isomers are either diradicals or have nearly zero singlet-triplet splittings. These species are expected to polymerize, forming insoluble solids. The classification of fullerenes according to their gap is analyzed, and computational methods for treating small gap cases are discussed.