Colloidal particles can crystallize into a wide range of different structures. One way of tuning the crystal structure they form is by modifying their shape. Nanoparticles can be created in a huge variety of shapes, often corresponding to simple polyhedra. Polyhedral particles of a single shape and size can form a huge variety of crystal phases, and this variety will become even larger if we mix different types of polyhedra together. Recent experiments at LPS showed the self-assembly of a mixture of tetrahedra and octahedra into a densely packed crystal. To guide future experiments, it would be helpful to know combinations of shapes that readily self-assemble into well-defined crystal phases with interesting structures. In this project, you will use computer simulations to explore crystallization in mixtures of polyhedra. The goal is to identify candidate structures consisting of polyhedra, and identifying conditions where self-assembly can reliably take place. For interesting structures, you will also probe the thermodynamic stability of the crystal phases using either theoretical approximations or direct coexistence simulations. The ideal candidate has a strong background in statistical physics, as well as an interest in coding and/or computer simulations.