A new configuration is proposed for spherical hohlraums on OMEGA in which seven laser entrance holes (LEHs) are used—five around the equator and one at each pole [Farmer et al., Phys. Plasmas 26, 032701 (2019)]. This is known as the PEPR (pentagonal prism) hohlraum. A new view-factor code LORE is used to model the PEPR hohlraum and compare its performance with tetrahedral hohlraums shot on OMEGA. With optimization of beam pointings, the PEPR hohlraum produces a nonuniformity ranging from 1.1% (rms) at low albedos to 0.6% at high albedos. The tradeoffs between hohlraum-to-capsule ratio, uniformity, and background radiation temperature have been explored, and it has been shown that larger LEH radii on the poles can result in a modest improvement in uniformity. The seven-hole PEPR hohlraum is well matched to the OMEGA symmetry and promises to provide insight into the performance of spherical hohlraums including octahedral (six-LEH) hohlraums.