  In this work, we study the effects of mechanical anisotropy in a 2D
optomechanical crystal geometry. We fabricate and measure devices with
different orientations, showing the dependence of the mechanical spectrum and
the optomechanical coupling with the relative angle of the device to the
crystallography directions of silicon. Our results show that the device
orientation strongly affects its mechanical band structure, which makes the
devices more susceptible to fabrication imperfections. Finally, we show that
our device is compatible with cryogenic measurements reaching ground state
occupancy of 0.2 phonons at mK temperature.
