[en] The three-dimensional (3D) faceting morphology of ceria nanoparticles is analysed using transmission electron microscopy (TEM)-based computed tomography on the nanometre scale. A novel tomography mode of electron energy loss spectroscopic imaging using a single energy window for inelastically scattered electrons is introduced and found to be reliable and fast for freestanding nanoparticles. To compare the new tomographic method with other methods, we provide the first comprehensive application of three complementary TEM-based imaging techniques, including bright field TEM and annular dark field specific TEM (STEM). Traditional bright-field TEM tomography is found to be applicable, in spite of obvious artefacts, for crystalline particles of constant composition. However, the safest interpretation is achieved by a combined recording of bright field and spectroscopic images