The structure and stability of four possible isomers of C and BN have been investigated by means of ab initio calculations at the MP2/DZP level. The four geometries are a monocyclic ring, a graphite-like sheet and two fullerene structures. For C it is found that the graphite-like isomer is lowest in energy, while a BN fullerene consisting of 4- and 6-membered rings appears to be quite stable. It is possible that this fullerene plays the same role for boron nitride as C does for carbon.