The search of materials harder than diamond is long since a favourite subject in materials science. Moreover, atomic-scale porous materials, molecular sieves and insertion compounds are extensively investigated for their technological potential. We report on the recent work, mostly theoretical, on a restricted class of novel diamond-like carbon crystals which combine a large nanoscale porosity and high stability with a comparatively large stiffness. These studies naturally extend to other four-fold coordinated covalent elemental materials, e.g., to silicon clathrates. We review the theory of hollow sp3 lattices which are obtained from the coalescence or assembling of small fullerenes, with a theoretical description of the topology, structure, stability, elastic properties and electronic states of hollow diamonds. We conjecture about the possibility of fractal and quasicrystalline covalent structures of pure sp3 type. Finally we discuss the possible routes to experimentally realize such novel structures with the support of recent large-scale tight-binding molecular dynamics studies on the structural transformations of solid fullerite under laser irradiation.