A theoretical analysis of structures of diamond-like phases which are obtained from single-walled carbon nanotubes and three-dimensional graphites is performed. As a result of the analysis, the possibility of stable existence of thirteen phases in which carbon atoms are in crystallographically equivalent positions is established. We have found two novel chiral phases, precursors of which are three-dimensional graphites. Using the density functional theory method in the generalized gradient approximation, geometrically optimized structures for all phases are calculated, as well as cohesive energies, electron densities of states, bulk moduli, hardness, and X-ray powder diffraction patterns. The chemical composition of diamond-like phases is identical; however, their properties vary within wide ranges.