Two different types of irradiation systems based on dodecahedral configuration are proposed for 60, 72, 80, and 92 beams. By optimizing the system, it is expected that enough uniformity (≤1% rms) is provided. Furthermore, it is quantitatively discussed that the number of beams, power imbalance, and the beam pattern must be improved synchronously for a high illumination uniformity. ©1995 American Institute of Physics.