Graphene cones may be regarded as the noblest realization of the cone shape in graphite. Macroscopically they di£er from a sheet of graphite-graphene-only by their curvature. In graphene, however, the carbon atoms are arranged in a °at hexagonal network, like a honeycomb, and this network cannot be embedded seamlessly on a conical surface without deformation of the hexagonal faces. Obviously, if such an arrangement was possible to force into place, it would decay back to its °at equilibrium state the moment the force was gone. So how are the carbon atoms in the graphene cones arranged? Although direct examination through a microscope is not easily done, there is strong experimental and theoretical evidence that their seamless carbon networks are hexagonal, except at the tips, where there are one or more non-hexagonal faces.