Structural and spectroscopy parameters of C-6 are determined with ab initio calculations confirming the existence of nine isomers, Those geometries with high stability (the linear, where the electronic ground state is a triplet (X-3 Sigma(-)(g)), and the slightly distorted cyclic singlet (X(1)A(1)')) are determined with CASPT2/CASSCF. The effect of the correlation energy on the isomer stability is discussed. The local potential energy surfaces of the first electronic states of linear-C-6 are determined with CASPT2/CASSCF calculations and the ANO-L C[4s3p2d1f] basis set. We provide minimum energy geometries and excitation energies for 19 electronic states. A new assignment of the electronic spectrum transitions involving high-energy symmetry states is proposed. Electron affinity and ionization potential have been computed to be EA = 3.97 eV and IP = 9.73 eV.