Lawrence Berkeley National Laboratory

Understanding how polyhedra pack into extended arrangements is integral to the design and discovery of crystalline materials at all length scales1?3. Much progress has been made in enumerating and characterizing the packing of polyhedral shapes4?6, and the self-assembly of polyhedral nanocrystals into ordered superstructures7?9. However, directing the selfassembly of polyhedral nanocrystals into densest packings requires precise control of particle shape10, polydispersity11, interactions and driving forces12. Here we show with experiment and computer simulation that a range of nanoscale Ag polyhedra can self-assemble into their conjectured densest packings6. When passivated with adsorbing polymer, the polyhedra behave as quasi-hard particles and assemble into millimetre-sized three-dimensional supercrystals by sedimentation. We also show, by inducing depletion attraction through excess polymer in solution, that octahedra form an exotic superstructure with complex helical motifs rather than the densest Minkowski lattice13. Such large-scale Ag supercrystals may facilitate the design of scalable three-dimensional plasmonic metamaterials for sensing14,15, nanophotonics16 and photocatalysis17.