Abstract:We present the results of Monte Carlo simulations on a system of hard ellipsoids of revolution with length-to-breadth ratios a/b = 3, 2·75, 2, 1·25 and b/a = 3, 2·75, 2, 1·25. We identify four distinct phases, viz. isotropic fluid, nematic fluid, ordered solid and plastic solid. The coexistence points of all first order phase transitions are located by performing absolute free energy computations for all coexisting phases. We find nematic phases only for a/b ⩾ 2·75 and a/b ⩽ 1>/2·75. A plastic solid is only observed for 1·25 ⩾ a/b ⩾ 0·8. It is found that the phase diagram is surprisingly symmetric under interchange of the major and minor axes of the ellipsoids.