We present the phase diagram of hard snowman-shaped particles calculated using Monte Carlo simulations and free energy calculations. The snowman particles consist of two hard spheres rigidly attached at their surfaces. We find a rich phase behavior with isotropic, plastic crystal, and aperiodic crystal phases. The crystalline phases found to be stable for a given sphere diameter ratio correspond mostly to the close packed structures predicted for equimolar binary hard-sphere mixtures of the same diameter ratio. However, our results also show several crystal-crystal phase transitions, with structures with a higher degree of degeneracy found to be stable at lower densities, while those with the best packing are found to be stable at higher densities. (C) 2012 American Institute of Physics.