The results of ab initio calculations of the structure and properties of thirteen carbon diamond like phases with atoms located in equivalent crystallographic sites have been presented. The calculations have been performed by the B3LYP GGA method. Nine of the studied phases have been obtained by linking or combining nanotubes, the other four phases have been formed from three dimensional graphites. Two new spiral phases SA3 and SA4 whose precursors are 3D graphites have been studied for the first time. For all phases, structural characteristics, sublimation energies, electron densities of states, and bulk moduli have been determined. The X ray powder diffraction patterns required for identifying new diamond like phases in synthesized carbon materials have also been calculated.