Our paper has just been published in Nano Letters.
Pentagonal packing is a long-standing and rich mathematical topic: in two dimensions, the optimal (highest packing fraction η=0.921) packing of regular pentagons is a double-lattice arrangement, called the "pentagonal ice ray".
We pack pentagonal nanoprism into long-range mesocrystals by evaporation induced self-assembly and find the ice-ray structure, but also an arrangement devised by Albrecht Dürer in the 16th century, with a slightly lower packing fraction (η=0.854), as well as intermediate polymorphs that can be obtained by a continuous sliding transformation between these two configurations.
We discuss the subtle relation between the orientational and positional order, as well as the presence of defects in the lattices.
