  A new ultra-hard rhombohedral carbon rh-C4 (or hexagonal h-C12) is reported
as derived from 3R graphite through crystal chemistry construction and ground
state energy within the density functional theory. An extended hexagonal
three-dimensional network of h-C12 is formed of C4 tetrahedra alike in h-C4
lonsdaleite (hexagonal diamond). The electronic band structure of rh-C4 is
characteristic of insulator with Egap = 4 eV similarly to diamond. From the set
of elastic constants a larger value of bulk modulus versus lonsdaleite, and the
largest Vickers hardness (HV) versus both forms of diamond were derived.
