New structural forms of carbon have been discovered in recent years, the most notable being the fullerenes and nanotubes. The notion that curvature is readily accommodated by graphite sheets has led to speculation about other possible topologies that incorporate pentagons or heptagons in hexagonal graphite nets. by consideration of Euler’s theorem and the symmetry of a graphite sheet, five conical structures can be predicted. If pentagonal defects only are present, cone angles are completely determined by the total number of pentagons, n, where 0≤n≤6 for open structures. In the absence of heptagons, growth of any graphitic structure containing more than 6 pentagons leads inevitably to the closed n =12 form. Consequently, five cone angles are possible, with disk (n=0) and tubular (n=6) forms representing the end-members of the topological series. Ge and Sattler1 have observed the smallest-angle member of this series with a cone angle of 19.2° (n=5).