The structure of the Keggin-type beta-[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 alpha-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 beta-PW12 isomer always remains ca. 100 mV more positive than that of the beta-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 alpha and beta 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. W-183 NMR spectra of the oxidized forms of the PW12 isomers are acid dependent and in the case of beta-PW12 imply that the bridging oxygens between the W-I and W-II units are preferentially protonated in acidic media. EPR data on frozen solutions of one-electron reduced beta-[(PWW11O40)-W-V-O-VI](4-) indicate that either the W-I or the W-III unit in beta-PW12 is reduced in the beta-[(PW12O40)-O-VI](3-)/beta-[(PWW11O40)-W-V-O-VI](4-) process. In the absence of acid, reversible potentials obtained from the alpha- and beta-isomers of PW12 and [SiW12O40](4-) exhibit a linear relationship with solvent properties such as Lewis acidity, acceptor number, and polarity index.