Combining an efficient simulated annealing scheme for generating closed, hollow, spheroidal cage structures with a tight-binding molecular-dynamics method for energy optimization, the ground-state structure of every even-numbered carbon fullerene from C72 to C102 is determined. As a general trend, most ground-state structures of the large fullerenes have relatively low symmetries. In many cases, several isomers of a fullerene are found to have competitively low energies, which suggests that a mixture of these isomers can be observed in experimental prepared samples.