Using Monte Carlo and molecular dynamics simulations, we investigate the equilibrium phase behavior of a monodisperse system of Mackay icosahedra. We define the icosahedra as polyatomic molecules composed of a set of Lennard-Jones subparticles arranged on the surface of the Mackay icosahedron. The phase diagram contains a fluid phase, a crystalline phase, and a rotator phase. We find that the attractive icosahedral molecules behave similar to hard geometric icosahedra for which the densest lattice packing and the rotator crystal phase have been identified before. We show that both phases form under attractive interactions as well. When heating the system from the dense crystal packing, there is first a transition to the rotator crystal and then another to a fluid phase.

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