Rummaging through my Dropbox I came across a video of a simulation I ran in graduate school of the nucleation of hard polyhedra. This is an example of how excluded volume (the only interactions between the octahedra is that they do not overlap) can lead to the formation of an ordered system. The octahedra are placed in a box with fixed number, fixed volume (so fixed density of around 56%), and allowed to move. Eventually the system undergoes a phase transition from a disordered initial state to a crystalline arrangement.

This system serves as an analog of systems of weakly interacting, identically sized metal nanoparticles, which themselves can self-assemble into crystals by controlling their environmental conditions.

An example system of octahedra assembling from Henzie et al 2012. Scale bar is 500nm.

For a possibly quite lengthy conversation on self-assembling systems and particularly hard polyhedra feel free to contact me and ask.