Symmetrization of the radiation field inside hohlraum targets for indirectly driven heavy ion beam inertial confinement fusion (ICF) is investigated numerically. The targets considered consist of a casing, enclosing the spherical fuel capsule, and a few cylindrical radiators, schematically representing ion beam irradiated converters. Radiation absorption and re-emission are dealt with as in the paper by Murakami and Meyer-ter-Vehn (Nucl. Fusion 31 (1991) 1333), but with the geometry extended to three dimensions and with the finite size of the radiators taken into account. It is found that, for a practical casing to capsule area ratio (of the order of ten) and practical converter aspect ratios, two converters (allowing for two-side axisymmetric irradiation) cannot provide the uniformity required for ICF. However, with a spherical casing with six converters (placed in couples along the axes of a Cartesian co-ordinate system) it would be possible to illuminate a capsule with a non-uniformity well below 2%, which could satisfy the ICF requirements. The effects of changing the area ratio, the size and position of the converters and the geometry of the hohlraum are also discussed