  Colloidal cuboids have the potential to self-assemble into biaxial liquid
crystal phases, which exhibit two independent optical axes. Over the last few
decades, several theoretical works predicted the existence of a wide region of
the phase diagram where the biaxial nematic phase would be stable, but imposed
rather strong constraints on the particle rotational degrees of freedom. In
this work, we employ molecular simulation to investigate the impact of size
dispersity on the phase behaviour of freely-rotating hard cuboids, here
modelled as self-dual-shaped nanoboards. This peculiar anisotropy, exactly in
between oblate and prolate geometry, has been proposed as the most appropriate
to promote phase biaxiality. We observe that size dispersity radically changes
the phase behaviour of monodisperse systems and leads to the formation of the
elusive biaxial nematic phase, being found in an large region of the packing
fraction vs polydispersity phase diagram. Although our results confirm the
tendencies reported in past experimental observations on colloidal dispersions
of slightly prolate goethite particles, they cannot reproduce the direct
isotropic-to-biaxial nematic phase transition observed in these experiments.
