The relative energies of beta Keggin heteropolytungstates, Xn+W12O40(8-n)-, decrease as Xn+ is varied within period 3, from P5+ to Si4+ to Al3+. With heating of alpha-H5Ga3+W12O40 at 200 degrees C in water, an equilibrated mixture of alpha (T-d; one W-183 NMR signal) and beta (C-3v; three signals; 1:2:1 ratio) isomers is obtained. From Delta G(exp) = -RT In Kbeta ->alpha, in which (from Ga-71 NMR spectra) Kbeta ->alpha (= [alpha]/[beta]) = 5.0, beta-GaW12O405- is 0.65 kcal mol(-1) higher in energy than alpha-GaW12O405-. This finding is evaluated by analysis of the X-ray crystal structure alpha-K2Na3[GaW12O40]center dot 9.3H(2)O [trigonal, space group P3(2)21, a = 18.9201(13) angstrom, b = 18.9201(13) angstrom, c 12.5108(12) angstrom, Z = 3, T = 100(2)K], comparison of the Shannon and Prewitt radii and Pauling electronegativities of Al3+ and Ga3+, and insight from density functional theory calculations, which predicted E-beta - E-alpha = 0.32 kcal mol(-1).