Do cylinders exhibit a cubatic phase?

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.