[en] Monte Carlo simulations of a system of two-dimensional hard, homonuclear dimers are reported. The equation-of-state, structural and orientational properties, and the free energy were computed for the fluid phase and several crystalline and non-crystalline (non-periodic) solid structures. The differences in the Gibbs free energy between the various solid structures were found not to exceed 0.1k_BT per particle. This is much less than the contribution to the entropy per particle due to degeneracy of the 'ground state' of the non-periodic solid which amounts to 0.857k_BT. Hence, the thermodynamically stable solid structure of the system corresponds to a set of non-periodic arrangements of the molecular centres of mass and orientations. The coexistence pressure of the non-periodic solid and fluid is determined; it is located within the observed narrow hysteresis region. It is shown that structures of the crystalline solids are well approximated by a simple lattice model. (author). 40 refs, 15 figs, 7 tabs