Graphite, when vaporized by laser irradiation, produces a very stable cluster of 60 carbon atoms which, it has been suggested, takes the uniquely elegant form of one of the archimedian semiregular polyhedra - the truncated icosahedron1,2. In considering the possibility of other structures of especial stability, we are led by a sequence of fairly general arguments to consider a relatively restricted family of high-symmetry cage structures, which correspond to novel convex polyhedra of icosahedral symmetry. Considering each of the smaller (computationally accessable) species in the family we predict here that C20 is unstable; C80 and C140 have moderate resonance energies but are open shell; and C60, C 180 and C240 are closed shell especially stable forms. The latter two are possible stable carbon cages not yet experimentally characterized. 1986 Nature Publishing Group.
