The structure of the Keggin-type β-[PW12O40]3- (PW12) polyoxometalate, with n-Bu4N+ as the countercation, has been determined for the first time by single-crystal X-ray analysis and compared to data obtained from a new determination of the structure of the α-PW12 isomer, having the same countercation. Analysis of cyclic voltammograms obtained in CH3CN (0.1 M [n-Bu4N][PF6]) reveals that the reversible potential for the β-PW12 isomer always remains ca. 100 mV more positive than that of the α-PW12 isomer on addition of the acid CF3SO3H. Simulations of the cyclic voltammetry as a function of acid concentration over the range 0-5 mM mimic experimental data exceptionally well. These simulation-experiment comparisons provide access to reversible potentials and acidity constants associated with α and β fully oxidized and one- and two-electron reduced systems and also explain how the two well-resolved one-electron W(VI)/W(V) processes converge into a single two-electron process if sufficient acid is present. 183W NMR spectra of the oxidized forms of the PW12 isomers are acid dependent and in the case of β-PW12 imply that the bridging oxygens between the WI and WII units are preferentially protonated in acidic media. EPR data on frozen solutions of one-electron reduced β-[PWVWVI11O40]4- indicate that either the WI or the WIII unit in β-PW12 is reduced in the β-[PWVI12O40]3-/β-[PWVWVI11O40]4- process. In the absence of acid, reversible potentials obtained from the α- and β-isomers of PW12 and [SiW12O40]4- exhibit a linear relationship with solvent properties such as Lewis acidity, acceptor number, and polarity index.