Six different levels of theory agree in predicting a C-62 cage with one heptagonal, 13 pentagonal, and 19 hexagonal rings to be of lower total energy than all 2385 "classical" 12-pentagon fullerene isomers. At the LDA level of density functional theory the nonclassical structure, which uniquely has three pentagon-pentagon and five pentagon-heptagon edges, is more stable than its nearest fullerene rival by 36 kJ mol(-1).