The complete set of 271 classical fullerene isomers Of C-50 has been studied by full geometry optimizations at the SAM1, PM3, AM1, and MNDO quantum-chemical levels, and their lower energy structures have also been partially computed at the ab initio levels of theory. A D-5h species, with the least number of pentagon adjacency, is predicted by all semiempirical methods and the HF/4-31G calculations as the lowest energy structure, but the B3LYP/6-31G* geometry optimizations favor a D-3 structure (with the largest HOMOLUMO gap and the second least number of adjacent pentagons) energetically lower (-2 kcal/mol) than the D5h isomer. To clarify the relative stabilities at elevated temperatures, the entropy contributions are taken into account on the basis of the Gibbs energy at the HF/4-31G level for the first time. The computed relative-stability interchanges show that the D3 isomer behaves more thermodynamically stable than the D-5h, species within a wide temperature interval related to fullerene formation. According to a newly reported experimental observation, the structural/energetic properties and relative stabilities of both critical isomers (D-5h, and D-3) are analyzed along with the experimentally identified decachlorofullerene C50Cl10 of D-5h symmetry. Some features of higher symmetry C-50 nanotube-type isomers are also discussed.