Dual photoelastic modulator polarimeter systems are widely used for the measurement of light beam polarization, most often described by Stokes vectors, that carry information about an interrogated sample. The sample polarization properties can be described more thoroughly through its Mueller matrix, which can be derived from judiciously chosen input polarization Stokes vectors and correspondingly measured output Stokes vectors. However, several sources of error complicate the construction of a Mueller matrix from the measured Stokes vectors. Here we present a general formalism to examine these sources of error and their effects on the derived Mueller matrix, and identify the optimal input polarization states to minimize their effects in a dual photoelastic modulator polarimeter configuration. The input Stokes vector states leading to the most robust Mueller matrix determination are shown to form Platonic solids in the Poincaré sphere space; we also identify the optimal 3D orientation of these solids for error minimization.