Using isobaric Monte Carlo simulations, we map out the entire phase diagram of a system of hard cylindrical particles of length $L$ and diameter $D$, using an improved algorithm to identify the overlap condition between two cylinders. Both the prolate $L/D>1$ and the oblate $L/D<1$ phase diagrams are reported with no solution of continuity. In the prolate $L/D>1$ case, we find intermediate nematic textrm{N} and smectic textrm{SmA} phases in addition to a low density isotropic textrm{I} and a high density crystal textrm{X} phase, with textrm{I-N-SmA} and textrm{I-SmA-X} triple points. An apparent columnar phase textrm{C} is shown to be metastable as in the case of spherocylinders. In the oblate $L/D<1$ case, we find stable intermediate cubatic textrm{Cub}, nematic textrm{N}, and columnar textrm{C} phases with textrm{I-N-Cub}, textrm{N-Cub-C}, and textrm{I-Cub-C} triple points. Comparison with previous numerical and analytical studies is discussed. The present study, accounting for the explicit cylindrical shape, paves the way to more sophisticated models with important biological applications, such as viruses and nucleosomes.
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