The polymorphic relationships of the pure rare-earth oxides have been reinvestigated using X-ray diffraction methods for identification of phases. The oxides of the trivalent rare earth ions crystallize in three different types: A, B, and C. Each oxide has only one truly stable polymorph: La2O3, Ce2O3, Pr2O3, and Nd2O3 belong to the A type; Sm2O3, Eu2O3, and Gd2O3 to the B type; Tb2O3, Dy2O3, Ho2O3, Er2O3, Tm2O3, Yb2O3, and Lu2O3 to the C type. In addition Nd2O3, Sm2O3, Eu2O3, and Gd2O3 have low-temperature, apparently metastable, C-type polymorphs. The low-temperature form inverts irreversibly to the stable form at increasingly higher temperatures for decreasing cation radius.