The superdense hexagonal boron pnictides BX (X = As, Sb, Bi), whose structures are formed by distorted tetrahedra and characterized by a quartz-derived (qtz) topology, have been predicted from first principles as potential high-pressure phases. From full geometry structure relaxation and ground state energy calculations based on quantum density functional theory (DFT), qtz BX was found to be mechanically (elastic constants) and dynamically (phonons) stable. From the energy–volume equations of state, at high but experimentally accessible pressures, qtz boron pnictides were found to be more energetically favorable than corresponding cubic zinc–blende phases with diamond-like (dia) topology. According to the electronic band structures, the zinc–blende BX have larger band gaps than the qtz phases, which can be attributed to the higher covalence of the latter. A metallic behavior is only observed for qtz BBi, which is related to the dynamic instability as it follows from the phonon band structure.