The oxidation reaction of UO2 into U3O8 is studied as a function of the crystalline distortion of interstitial oxygen clusters, named cuboctahedra, which appear in U4O9 and U3O7 intermediate phases. For that purpose, the refinement of alpha-U4O9 was performed because this phase undergoes a trigonal distortion from cubic beta-U4O9 when the temperature is decreased. In alpha-U4O9, the cuboctahedra can be described as crumpled sheets taken from a fragment of U3O8. The manner by which the accumulation of crumpled sheets can lead to the formation of U3O8 is discussed.