Carbon is an element that is unique in the variety, utility and individuality of its allotropes. Diamond and graphite each have several uniquely extreme properties that have been exploited in twentieth century science and technology. Against the curious landscape of the periodic table the discoveries of fullerenes (1985) and nanotubes (1991) stand out as substantial landmarks. Their beauty lies in creating isolatable molecular forms. In the somewhat messier world of crystal defects, similar topological concepts can be applied, leading to sheets which are buckled, folded, 'welded' together, or unified into one sheet. The description of these defects comes from the science of dislocations, and their structures can be deduced from first principles methods, such as density functional theory (DFT). A connector between sheets, similar to the ramp connecting the floors of a multistorey car park, is a prismatic screw dislocation dipole. A fold is a pile-up of basal dislocation dipoles. The identification and characterization of dislocations in graphite, gives insight into structures which have been overlooked in the science of graphite, especially radiation damage which occurs in reactor graphite subjected to energetic neutrons.