  Emergent behaviors occur in a vast array of systems across many scales, and
are of fundamental physical importance because of the intrinsic difficulty in
linking microscopic system properties to macroscopic behaviors. Here we study
the emergent self-assembly behavior of model systems of recently synthesized
families of concave dimpled hard spheres, or lock-and-key colloids. We find
that as dimple size increases each family exhibits a crossover from a structure
that does not reflect the particle symmetry to one that does and, surprisingly,
the point at which this crossover occurs is approximately independent of the
particle symmetry. Using a combination of numerical and analytic techniques we
study systems at infinite and finite pressure, and find different common
control parameters in each limit. Our results suggest there exists a set of
experimentally realizable colloidal systems that exhibit complex emergent
behaviors that can be traced to a common underlying microscopic control
parameter.
