Spherical Codes
Here we provide supplemental material for the paper Phillips, Jankowski, Jyoti Krishnatreya, Edmund, Sacanna, Grier, Pine, Glotzer, Digital Colloids: Reconfigurable Clusters as High Information Density Elements, Soft Matter, 2014. In the materials indexed in the navigation panel on the left, we show the rearrangement and transition structures found for each N = 4-12 cluster. Movies of the transition structures were captured at the central-to-halo diameter ratio where the cluster was first observed to have a measurably mobile HP structure (See figures SI-I-2 and SI-I-3).
For each cluster we note the rotational symmetry of the cluster, as well as the number of ways that each rearrangement can occur. In each case, the number of ways is consistent with a subgroup of the rotational symmetry group of the cluster. In each case, the cluster after the rearrangement is still in the same spherical code-like structure, just with a permutation of the assignation of lattice points to spheres. (Note, For the movies, the timestep/frame is not kept constant between movies but is constant within a movie.)