Density Landscapes and Crystal Transitions for Self-Assembly of Continuous Families of Shapes

Dense packings of hard polyhedra have been studied for centuries due to their mathematical aesthetic and more recently for their applications in fields such as granular matter, amorphous matter, and biology. The spontaneous organization of hard polyhedral colloids in solution has only recently been addressed, demonstrating a plethora of assembled complex structures. For any given shape, the densest packings and the structures assembled spontaneously from the fluid are often different. In this talk we investigate, through computer simulations, connections between packings and assemblies for three families of convex polyhedra. We discuss  the possibility of predicting one from knowledge of the other, transitions between crystals as a function of the building block shape, discuss trends, and link with previous works.