  Since the 1920s, packing arguments have been used to rationalize crystal
structures in systems ranging from atomic mixtures to colloidal crystals.
Packing arguments have recently been applied to complex nanoparticle
structures, where they often, but not always, work. We examine when, if ever,
packing is a causal mechanism in hard particle approximations of colloidal
crystals. We investigate three crystal structures comprised of their ideal
packing shapes. We show that, contrary to expectations, the ordering mechanism
cannot be packing, even when the thermodynamically self-assembled structure is
the same as that of the densest packing. We also show that the best particle
shapes for hard particle colloidal crystals in the infinite pressure limit are
imperfect versions of the ideal packing shape.
