The inequivalence in surface oxygen distance and Pt-Pt bond length are less notable with the Pt6Ox stoichiometries due to the increase in degrees of freedom, which allow the particle to adapt better to the surface. However, the tendency to form linear O-Pt-O bonds still proves to be significant since the observed minima include these motifs in all their structures, often bonding using O atoms from the ceria lattice to construct these linear motifs. For low and medium oxidation states, the particles form more compact structures (e.g., Pt6O9/CeO2(111)) where O atoms are shared between multiple platinum atoms.