Two solid phases of cyclohexane have been investigated over a temperature range spanning 13-266 K on a powdered, perdeuterated sample using neutron total scattering. Phase II has an ordered structure (C2/c) that forms below 186 K. Between 186 and 280 K it exists as a plastic solid-phase I (Fm3m), where the molecules are rotationally disordered about the lattice points of the face-centred cubic cell. Data-dependent atomistic configurations that represent the 'instantaneous' crystal structure have been generated from the total scattering data using reverse Monte Carlo refinement. Analysis of the local structure reveals that instantaneous distortions in phase I resemble the average structure of phase II.