The structural characteristics and properties of three new carbon phases (LA9, LA10, CA12), which have a diamond-like structure and atoms located in crystallographically equivalent positions, are described. The model mechanism of LA9 and LA10 formation is the linking of L6 and L4–8 graphene layers, respectively, and phase CA12 can be formed by linking C4 tetrahedral clusters. Phases LA9, LA10, and CA12 can also be formed as a result of the polymorphic transformations of three-dimensional graphite phases, when all atoms transform from a three-coordinated into a four-coordinated state. LDA-DFT calculations of the LA9, LA10, and CA12 phases are used to find their geometrically optimized structures and properties (density, total energy, density of states). In addition, powder X-ray diffraction patterns are calculated for these phases and possible methods of their synthesis are analyzed.