Keggin heteropolyanions [XM(12)O(40)](n-) have various isomeric structures, alpha and beta being the most common. Conventionally, the alpha structure appears to be the most stable, but calculations carried out at the DFT level for X = P(V), Si(IV), Al(III), As(V), Ge(IV), and Ga(III) and M = W(VI) and Mo(VI) show that this stability depends on several factors, particularly on the nature of the heteroatom (X) and the total charge of the cluster. In this paper, we apply the clathrate model to the Keggin molecule to carry out a fragment-interaction study to elucidate when and why the traditional relative stability of various isomers can be inverted. The fully oxidized anions that have inverted the traditional stability trend in this series are [AlW(12)O(40)](5-) and [GaW(12)O(40)](5-), both of which contain a third-group heteroatom and an overall charge of -5. beta-isomers are always more easily reduced than alpha-isomers. This experimental observation suggests that reduction favors the stability of beta-isomers and one of the most important results of this study is that the alpha/beta inversion is achieved in most cases after the second reduction. The alpha- and beta-isomers may have different properties because the energy of the LUMO, a symmetry-adapted d(xy)-metal orbital, is different.