For the free-standing structures and the ceria-supported Pt3Ox, the most stable structure at ΔμO=0 eV (T= 0K) is the structure with the Pt3O5 stoichiometry. For the freestanding Pt6Ox system, Pt6O6 is the most stable configuration at ΔμO=0 eV, probably due These results indicate that the ceria surface contributes to stabilizing more oxidized states of the PtOx particles for some regions of the phase diagrams, but stabilizes more Odeficient states for others. A general stabilization of more O-deficient states would be expected due to the oxidizing behavior of the ceria surface, but our calculated phase diagrams demonstrate that intricate effects related to the kind of structures and structural motifs that each stoichiometry can form are more relevant than the oxidizing capacity of ceria.