The nanoparticles built of bicontinuos lyotropic phases of cubic symmetry are studied within the framework of the Landau-Brazovskii functional that correctly predicts the structure of soft monocrystals and thin films of bicontinuos lyotropic phases. A detailed description of the geometry and topology of cubosomes is presented. This level of description of the internal structure of cubosomes is not easily accessible by experimental techniques. I show that the internal structure of the cubosomes may be extremely rich.