  Rhombohedral dense forms of carbon, rh-C2 (or hexagonal h-C6), and boron
nitride, rh-BN (or hexagonal h-B3N3), are derived from rhombohedral 3R graphite
based on original crystal chemistry scheme backed with full cell geometry
optimization to minimal energy ground state computations within the quantum
density functional theory. Considering throughout hexagonal settings featuring
extended lattices, the calculation of the hexagonal set of elastic constants,
provide results of large bulk moduli i.e. B0(rh-C2) = 438 GPa close to that of
diamond, and B0(rh-BN) = 369 GPa close to that of cubic BN. The hardness
assessment in the framework of three contemporary models enables both phases to
be considered as ultra-hard. From the electronic band structures calculated in
the hexagonal Brillouin zones, 3R graphite is a small-gap semiconductor,
oppositely to rh-C2 that is characterized by a large band gap close to 5 eV, as
well as the two BN phases.
