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Double-lattice packing of pentagonal gold bipyramids in supercrystals with triclinic symmetry


Pentagonal packing is a long-standing issue and a rich mathematical topic, brought to the fore by recent progress in nanoparticle design. Gold pentagonal bipyramids combine five-fold symmetry and anisotropy and their section varies along the length. In this work, we obtain colloidal supercrystals of pentagonal gold bipyramids in a compact arrangement that generalizes the optimal packing of regular pentagons in the plane. Multimodal investigations reveal a two-particle unit cell with triclinic symmetry, a lower symmetry than that of the building blocks. Monte Carlo computer simulations show that this lattice achieves the densest possible packing. Going beyond pentagons, further simulations show an odd-even effect of the number of sides on the packing: odd-sided bipyramids are non-centrosymmetric and require the double-lattice arrangement to recover inversion symmetry. The supercrystals display a facet-dependent optical response that is promising for sensing, metamaterials applications and for fundamental studies of self-assembly processes.