Attempts to understand the complex 3D morphology of non-lamellar liquid-crystalline nanostructured particles, formed by the dispersion of a reversed hexagonal phase (hexosomes) and bicontinuous cubic phase (cubosomes) in water, have been limited by the lack of suitable 3D imaging techniques. Using cryo-field emission scanning electron microscopy, we show that whereas the structure of cubosomes generally reflects that anticipated from modeling approaches, hexosomes, which were previously proposed to be flat hexagonal prisms, in fact often possess a "spinning-top-like" structure, which is likely to influence their interactions with surfaces.