Using density functional theory, the structures and properties of carbon diamond-like phases, all of whose atoms occupy equivalent crystallographic positions, were studied. Structures of these phases were obtained by linking or superposing ofcarbon clusters. It was found that thirteen such phases can exist. The calculated structural characteristics and properties (density, cohesive energy, bandgap, bulk modulus, hardness, and x-ray diffraction pattern) of the diamond-like phases under study differ significantly from respective parameters of cubic diamond.