We here report a systematic theoretical study on geometries, electronic structures, and energetic stabilities of six hexanuclear polyoxometalates [M6O19](2-) of the six-valence-electron metals including the d-elements M = Cr, Mo, W, Sg from group 6 and the f-elements M = Nd, U. Scalar relativistic density functional theory was applied to these clusters in vacuum and in solution. It is shown that the O-h Lindqvist structure of the isolated [M6O19](2-) units with hexavalent M elements (M+6) is only stable for the three heavy transition metals M = Mo, W, and Sg. The rare T-h symmetry is predicted for M = U both in vacuum and in solution, owing to pseudo-Jahn-Teller distortion of these closed-shell systems. The O-h and T-h structures correspond to cyclic "aromatic" U+O-U and alternating U-O-U bonding of cross-linked U4O4 rings, respectively. The reduced [U6O19](8-) duster with pentavalent U+5 also shows T-h symmetry in vacuum, but O-h symmetry in a dielectric environment. The occurrence of different structures for varying fractional oxidation states in different environments is rationalized. Theoretical investigation of the recently synthesized U+5 complex [U6O13L6](0) (L-6 = tetracydopentadienyl dibipyridine) shows a distorted T-h-type symmetry, too. The stabilities of these complexes of different metal oxidation states are consistent with the general periodic trends of oxidation states.