The existence of a novel octahedral UO(6) complex had been suggested by Pyykko et al. [Pyykko, P.; Runeberg, N.; Straka, M.; Dyall, K. G. Chem. Phys. Lett. 2000, 328, 415]. We have now investigated the stability, the geometric and electronic structures, and the vibrations of various UO(6) molecules, using spin-orbit density functional and scalar-relativistic coupled-cluster approaches. We find four different (meta-)stable species, namely (3)D(2h)-UO(2)(eta(2)-O(2)(*))(2) at lowest energy, (3)C(2v)-UO(4)(*)(eta(2)-O(2)(*)) and (1)D(3)-U(eta(2)-O(2))(3) at medium energies, and (1)O(h)-UO(6) at highest energy. The decay of O(h)-UO(6) occurs via an activated spin-flip mechanism. The UO(6) species correspond to local minima on singlet and triplet energy surfaces and might be trapped in noble gas matrices. Experimentally, the four species might be identified through their vibrational spectra. Uranium is best described as coordinated by oxygen atoms in various oxidation states as oxo O(2-), oxido(1) O(*-), peroxido O(2)(2-), and superoxido O(2)(*-) ligands. The occurrence of monovalent oxygen is remarkable. The resulting characterization of the central ion as U(VI) in all four cases does not fully reflect the electronic differences, nor the "valence-activity" of the U-6p(6) semicore shell.