  We study an experimental system of hard granular squares in two dimensions,
energized by vibration. The interplay of order in the orientations and
positions of anisotropic particles allows for a rich set of phases. We measure
the structure and dynamics of steady states as a function of particle density.
This allows us to identify a progression of phases in which a low density
isotropic fluid gives way to a phase with tetratic orientational order,
short-range translational correlations, and slowed rotational dynamics. In this
range of density we also observe a coupling between the molecular orientational
order and bond-orientational order. At higher densities, the particles freeze
into a translationally and orientationally ordered square crystalline phase in
which translational diffusion is suppressed.
