We have developed an experimental platform for the National Ignition Facility that uses spherically converging shock waves for absolute equation-of-state (EOS) measurements along the principal Hugoniot. In this Letter, we present one indirect-drive implosion experiment with a polystyrene sample that employs radiographic compression measurements over a range of shock pressures reaching up to 60 Mbar (6 TPa). This significantly exceeds previously published results obtained on the Nova laser [R. Cauble et al., Phys. Rev. Lett. 80, 1248 (1998)] at a strongly improved precision, allowing us to discriminate between different EOS models. We find excellent agreement with Kohn-Sham density-functional-theory-based molecular dynamics simulations.