  We investigate the possibility that freely rotating cylinders with an aspect
ratio $L/D=0.9$ exhibit a cubatic phase similar to the one found for a system
of cut-spheres. We present theoretical arguments why a cubatic phase might
occur in this particular system. Monte Carlo simulations do not confirm the
existence of a cubatic phase for cylinders. However, they do reveal an
unexpected phase behavior between the isotropic and crystalline phase.
