  We perform Dynamic Monte Carlo simulations to investigate the equilibrium
dynamics of hard colloidal cuboids in oblate and prolate nematic liquid
crystals. In particular, we characterise the particles' diffusion along the
nematic director and perpendicularly to it, and observe a structural relaxation
decay that strongly depend on the particle anisotropy. To assess the
Gaussianity of their dynamics and eventual occurrence of collective motion, we
calculate two- and four-point correlation functions that incorporate the
instantaneous values of the diffusion coefficients parallel and perpendicular
to the nematic director. Our simulation results highlight the occurrence of
Fickian and Gaussian dynamics at short and long times, locate the minimum
diffusivity at the self-dual shape, the particle geometry that would
preferentially stabilise biaxial nematics, and exclude the existence of
dynamically correlated particles.
