Radiation symmetrization within spherical, ellipsoidal and cylindrical hohlraum targets for heavy-ion inertial-confinement fusion (ICF) is studied by means of a 3D numerical static model, in which realistic assumptions are made concerning the geometry of the system and, particularly, of the radiation >. Among the systems so far studied, only spherical hohlraums with six converters achieve the illumination symmetry of the fusion capsule considered necessary for ICF applications. A parametric study of cylindrical hohlraums enlightens the effect of several parameter changes, and suggests directions for further studies, aiming at the design of two-converter targets.