where α and β are patches on particles i and j respectively, Fig. ). Throughout the simulations, σ LJ , which is normally the measure of the diameter of the interacting particles, was set to 0.6 Å. As each octahedra had unit length, this value is slightly larger than the minimum distance required for the two hard octahedra packed along the facets (0.5 Å). This is to allow for a small gap between the hard octahedra, which is likely to exist between the analogous two neighbouring cages due to their van der Waals radii. J is the measure of the interaction strength between the two octahedra and was chosen for each simulation such that k B T t ≈ 1 where T t is the transition temperature. The interaction parameters used are summarised in Tables and. The cutoff distance, r cut , is set to 1.8σ LJ so that the patches interact with nearest neighbour polyhedra only.