What is the best way to pack objects in space? 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 polyhedra 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. We investigate connections between packings and assemblies for families of convex polyhedra.  We investigate the possibility of predicting one from knowledge of the other, discuss trends, and link with previous works.  

• Publications:

1. Intermediate crystalline structures of colloids in shape space. Klotsa et al., Soft Matter 2018, DOI: 10.1039/C8SM01573B, (2018).

2. Clusters of polyhedra in spherical confinement. E. G. Teich, G. van Anders, D. Klotsa et al. PNAS 113, no 6, E669-678 (2016).

3. Complexity in surfaces of densest packings for families of polyhedra. E. R. Chen*, D. Klotsa*, et al. Phys. Rev. X 4, 011024 (2014). *contributed equally.

4. Understanding shape entropy through local dense packing. G. van Anders, D. Klotsa, et al. PNAS 111, no 45, E4812--E4821 (2014).

5. Press: physics.org (clusters), Synopsis, physicsworld and the New Scientist, "Material witness: The force of shape". P. Ball, Nature Materials 13, 1083 (2014) and physics.org (entropy).

6. Video:  Public talk at Columbia.