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Soft matter crystallography -- complex, diverse, and new crystal structures in condensed materials on the mesoscale

An increasing variety of crystal structures has been observed in soft condensed matter over the past two decades, surpassing most expectations for the diversity of arrangements accessible through classical driving forces. Here, we survey the structural breadth of mesoscopic crystals -- formed by micellar systems, nanoparticles, colloids etc. -- that have been observed both in soft matter experiments and coarse-grained self-assembly simulations. We review structure types that were found to mimic crystals on the atomic scale, as well as those that do not correspond to known geometries and seem to only occur on the mesoscale. While the number of crystal structure types observed in soft condensed matter still lags behind what is known from hard condensed matter, we hypothesize that the high tunability and diversity of building blocks that can be created on the nano- and microscale will render a structural variety that far exceeds that of atomic compounds, which are inevitably restricted by the "limitations" imposed by the periodic table of elements and by the properties of the chemical bond. An infusion of expertise in structural analysis from the field of crystallography into the soft condensed matter community will establish the common language necessary to report, compare, and organize the rapidly accruing structural knowledge gathered from simulations and experiments. The prospect of new materials created in soft matter and new, length-scale-spanning insights into the formation of ordered structures in both hard and soft condensed matter promise exciting new developments in the area of self-assembled mesoscale materials.