In the framework of a crystallochemical approach, new hexagonal (P63/mc) sp3-bonded BN polytypes (4H, 6H and 8H) and ternary BC2N were proposed by rationalized substitutions of C for B and N in hexagonal carbon allotrope C8 (4C carbon) with cfc topology, and density functional theory calculations of their ground states were performed. All new phases were found to be cohesive and stable mechanically (elastic constants) and dynamically (phonon band structures). According to modern models of hardness, the new phases were recognized as superhard with Vickers hardness above 50 GPa. Their electronic band structures exhibit insulating behavior with large band gaps.