Vickers hardness (H V ) has been predicted using four modern theoretical models. The thermodynamic (T) model , which is based on thermodynamic properties and crystal structure, shows surprising agreement with available experimental data and is therefore recommended for hardness evaluation of superhard and ultrahard phases . The Lyakhov-Oganov (LO) approach takes into account the topology of the crystal structure, the strength of covalent bonding, the degree of ionicity and directionality; however, in the case of ultrahard phases of light elements, this model gives underestimated hardness values . Two empirical models, Mazhnik-Oganov (MO) and Chen-Niu (CN) , use the elastic properties. Fracture toughness (K Ic ) has been evaluated within the Mazhnik-Oganov model . The results for the currently proposed hexagonal carbon allotropes and others from the literature are summarized in Tables and.