© 2016 Elsevier B.V. We have designed an experiment for the National Ignition Facility to measure the Hugoniot of materials such as plastic at extreme pressures. The design employs a strong spherically converging shock launched through a solid ball of material using a hohlraum radiation drive. The shock front conditions can be characterized using X-ray radiography until background from shock coalescence overtakes the backlit signal. Shock coalescence at the center is predicted to reach tens of Gbars and can be further characterized by measuring the X-ray self-emission and 2.45 MeV neutrons emitted from the shock flash region. In this simulation design work the standard plastic sphere is replaced with a deuterated polyethylene sphere, CD2, that reaches sufficiently high densities and temperatures in the central hot spot to produce neutrons from Deuterium-Deuterium (DD) fusion reactions that can be measured by a neutron time of flight spectrometer (nTOF) and act as a temperature diagnostic. This paper focuses on the design of these experiments, based on an extensive suite of radiation-hydrodynamics simulations, and the interpretation of the predicted DD neutron signals. The simulations predict mean temperatures of 1 keV in the central hot spot with mean densities of 33 g/cc and mean pressures of 25 Gbar. A preliminary comparison with early experimental results looks promising with an average ion temperature of 1.06 ± 0.15 keV in the central hot spot estimated from the nTOF spectral width and measured neutron yield of 7.0 (±0.5) × 109 DD neutrons.