  The successful development and optimisation of optically-driven micromachines
will be greatly enhanced by the ability to computationally model the optical
forces and torques applied to such devices. In principle, this can be done by
calculating the light-scattering properties of such devices. However, while
fast methods exist for scattering calculations for spheres and axisymmetric
particles, optically-driven micromachines will almost always be more
geometrically complex. Fortunately, such micromachines will typically possess a
high degree of symmetry, typically discrete rotational symmetry. Many current
designs for optically-driven micromachines are also mirror-symmetric about a
plane. We show how such symmetries can be used to reduce the computational time
required by orders of magnitude. Similar improvements are also possible for
other highly-symmetric objects such as crystals. We demonstrate the efficacy of
such methods by modelling the optical trapping of a cube, and show that even
simple shapes can function as optically-driven micromachines.
