BEYOND C-60 - GRAPHITE STRUCTURES FOR THE FUTURE

Geometric concepts are used to propose and study stable graphite struc tures with different curvatures. It is shown that graphite can decorat e surfaces which involve the three different geometries in three dimen sions: Euclidean with zero Gaussian curvature, spherical or ellipsoida l with positive Gaussian curvature, and hyperbolic with negative Gauss ian curvature. Fullerenes, graphite onions, carbon nanotubes, negative ly curved graphite, icosahedral glasses of C-60, molecular quasicrysta ls of fullerenes, and liquid crystals of C-60 are analysed. Some of th ese arrangements have already been found and others remain a challenge for the future.