Semi-empirical (MNDO) and ab-initio Hartree-Fock (3-21G) calculations on the structure and stability of C72 are reported. Though never isolated experimentally, C72 has been previously suggested to be a particularly stable fullerene based on simple Huckel molecular orbital ideas. However, our calculations which include complete geometry optimization definitively show that it is significantly less stable than C70. The structural and electronic factors which are responsible for its instability are discussed.