Assuming that rings of 5, 7 and 8 carbon atoms are allowable (as well as hexagons) in graphitic sheets, a great variety of finite and infinite structures can be postulated. Besides the shells of the fullerenes, which have positive Gaussian curvature and the cylinders which have zero Gaussian curvature, infinite periodic networks with negative Gaussian curvature are possible. The latter promise to have lower energies than the convex fullerenes.

http://dx.doi.org/10.1016/0008-6223(92)90066-6