Heuristic rules that allow identifying the preferred mixed-valence isomers and Jahn-Teller axis arrangements in the water oxidation catalyst [(Mn4O4)(V4O13)(OAc)(3)](n-) and its activated form [(Mn4O4)(V4O13)(OAc)(2)(H2O)(OH)](n-) are derived. These rules are based on computing all combinatorially possible mixed-valence isomers and Jahn-Teller axis arrangements of the Mn-III atoms, and associate energetic costs with some structural features, like crossings of multiple Jahn-Teller axes, the location of these axes, or the involved ligands. It is found that the different oxidation states localize on different Mn centers, giving rise to clear Jahn-Teller distortions, unlike in previous crystallographic findings where an apparent valence delocalization was found. The low barriers that connect different Jahn-Teller axis arrangements suggest that the system quickly interconverts between them, leading to the observation of averaged bond lengths in the crystal structure. We conclude that the combination of cubane-vanadate bonds that are chemically inert, cubane-acetate/water bonds that can be activated through a Jahn-Teller axis, and low activation barriers for intramolecular rearrangement of the Jahn-Teller axes plays an essential role in the reactivity of this and probably related compounds.