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A fundamental characteristic of matter is its ability to form orderedstructures under the right thermodynamic conditions. Predicting thesestructures - and their properties - from the attributes of a material'sbuilding blocks is the holy grail of materials science. Here, we investigatethe self-assembly of 145 hard convex polyhedra whose thermodynamic behaviorarises solely from their anisotropic shape. Our results extend previous workson entropy-driven crystallization by demonstrating a remarkably high propensityfor self-assembly and an unprecedented structural diversity, including some ofthe most complex crystalline phases yet observed in a non-atomic system. Inaddition to 22 Bravais and non-Bravais crystals, we report 66 plastic crystals(both Bravais and topologically close-packed), 21 liquid crystals (nematic,smectic, and columnar), and 44 glasses. We show that from simple measures ofparticle shape and local order in the disordered fluid, the class of orderedstructure can be predicted.

Structural diversity and the role of particle shape and dense fluid behavior in assemblies of hard polyhedra