For a structure to be considered a representative phase at any given simulation condition, we imposed a minimum cluster limit of 50 polyhedra before undergoing any further analysis. To ensure we were sampling from the bulk structure, the outer layer of the cluster is then removed before any subsequent analysis. To determine the different structural phases formed, we calculated and compared the radial distribution functions (RDFs) of the centres of each octahedra within the clusters. Although this removed the orientational behaviour of the different phases, structures with similar RDFs were visually inspected to ensure that the orientational behaviour led to no meaningful differences between the structures. For structures at low σ ang , we were able to determine the space group of the clusters by abstracting a unit cell and using FINDSYM , a program used to identify the space group of a crystal, on a coarse-grained version of the structure and converted the solved structure back onto the equivalent structure formed with the cages. An overview of this process is given in Section S3.