The present work represents a challenging prediction of new tetragonal and hexagonal boron nitrides, B 2 N 3 and B 3 N 3 , from crystal chemistry and first principles using original pentacarbon templates. The crystal chemistry investigations were supported by computations of the ground structures and energy-dependent quantities within the well-established framework of the quantum density functional theory (DFT). All new phases were found to be cohesive. The mechanical stability of the new phases, which follows from the calculated values of the elastic constants, is coupled with their extreme hardness, varying from 45 GPa for tet-B 3 N 3 to 52 GPa for both B 2 N 3 polymorphs. Dynamically, all new phases were found to be stable from positive phonon frequencies, and observed high-frequency modes were assigned to the short B-N distances in their crystal structures. Conductive electronic behavior is observed, which varies from small bandgap semiconducting h-B 2 N 3 , to weakly metallic tetragonal B 2 N 3 and B 3 N 3 , and finally to metallic h-B 3 N 3 . The results obtained are expected to inspire experimental attempts to synthesize new B-N phases at high pressures and high temperatures. ** calculated using isotropic approximation The additional yellow spheres result from the decrease in symmetry.