Table gives literature and currently calculated (in brackets) lattice constants after full unconstrained geometry optimizations. qtz C 3 is energetically less cohesive (E coh /atom = -1.37 eV/at.) than tricarbon formed with linear C-C-C building blocks found with E coh /atom = -1.55 eV eV/at. Also, as a general trend, all the allotropes examined here are less cohesive than cubic and hexagonal (lonsdaleite) diamond with E coh /atom = -2.46 eV/atom. By extending the carbon lattice, we identified a twice as large cell with single sixfold C positions in space group P6 5 22, No 179 for hexagonal C 6 . The calculated crystal data are given in Table and the structure is shown in Fig. . In qtz topology, C 6 is close to qtz C 3 , and the atomic averaged volumes are also close, although smaller in novel C 6 . We also include results obtained for 5-ring C 6 in unf topology such as unj C 3 (SACADA #29) .