Structure factors for small synthetic crystals of the C-type rare earth (RE) sesquioxides Y2O3, Dy2O3 and Ho2O3 were measured with focused λ = 0.7000 (2) Å, synchrotron X-radiation, and for Ho2O3 were re-measured with an MoKα (λ = 0.71073 Å) source. Approximate symmetry in the deformation electron density (Δρ) around a RE atom with pseudo-octahedral O coordination matches the cation geometry. Interactions between heavy metal atoms have a pronounced effect on the Δρ map. The electron-density symmetry around a second RE atom is also perturbed significantly by cation–anion interactions. The compounds magnetic properties reflect this complexity. Space group Ia{\bar 3}, cubic, Z = 16, T = 293 K: Y2O3, Mr
= 225.82, a = 10.5981 (7) Å, V = 1190.4 (2) Å3, Dx
= 5.040 Mg m−3, μ
0.7 = 37.01 mm−1, F(000) = 1632, R = 0.067, wR = 0.067, S = 9.0 (2) for 1098 unique reflections; Dy2O3, Mr
= 373.00, a = 10.6706 (7) Å, V = 1215.0 (2) Å3, Dx
= 8.156 Mg m−3, μ
0.7 = 44.84 mm−1, F(000) = 2496, R = 0.056, wR = 0.051, S = 7.5 (2) for 1113 unique reflections; Ho2O3, Mr
= 377.86, a = 10.606 (2) Å, V = 1193.0 (7) Å3, Dx
= 8.415 Mg m−3, μ
0.7 = 48.51 mm−1
F(000) = 2528, R = 0.072, wR = 0.045, S = 9.2 (2) for 1098 unique reflections of the synchrotron data set.
Local Approximate Symmetry of Birkhoff–James Orthogonality in Normed Linear Spaces