Based on superdense C6 with a quartz (qtz) topology, new ultrahigh-density hexagonal binary phases, qtz BN and qtz SiC, were identified via full geometry structure relaxations and ground state energies using calculations based on the quantum density functional theory (DFT) with a gradient GGA exchange–correlation XC functional. Like qtz C6, with respect to diamond, the resulting binary qtz BN and qtz SiC were found to be less cohesive than cubic BN and cubic SiC, respectively, but were confirmed to be mechanically (elastic constants) and dynamically (phonon band structures) stable. Higher densities of the new phases correlate with higher hardness values compared to cubic BN and cubic SiC. In contrast to the regular tetrahedra that characterize the cubic BN and SiC phases, the corner-sharing tetrahedra in the new phases are distorted, which accounts for their exceptional density and hardness. All three qtz phases were found to be semiconducting to insulators, with reduced band gaps compared to diamond, cubic BN, and cubic SiC.