The question of the lowest energy structure of the Cg molecule has been addressed using high level of theory ab initio methods such as the coupled cluster and multiconfiguration perturbation theory approaches. The results show that the linear cumulenic chain and the monocyclic six-membered ring structure with D-3h symmetry are very close in energy, indicating that both structures may be observed experimentally. The hexagonal six-membered ring structure of D-6h symmetry was confirmed as a saddle point geometry. These results are in partial contradiction with two earlier ab initio studies that either find the distorted hexagon structure [Raghavachari, Whiteside, and Pople, J. Chem. Phys. 85, 6623 (1986)] or the linear cumulenic chain [V. Parasuk and J. Almlof, J. Chem. Phys. 91, 1137 (1989)] to be the lowest energy structure.