  The existence of topological order is frequently associated with strongly
coupled quantum matter. Here, we demonstrate the existence of topological
phases in classical systems of densely packed, hard, anisotropic polyhedrally
shaped colloidal particles. We show that previously reported transitions in
dense packings lead to the existence of topologically ordered thermodynamic
phases, which we show are stable away from the dense packing limit. Our work
expands the library of known topological phases, whose experimental realization
could provide new means for constructing plasmonic materials that are robust in
the presence of fluctuations.
