Uniaxial ordering by self-assembly of isotropic octahedral junctions

We demonstrate that isotropic octahedral (sixfold branched) junctions with three diagonal end point pairs of different colors almost inevitably form a macroscopic assembly of uniaxial order, exhibiting the perfect order of a single color. Monte Carlo simulations of the antiferromagnetic three-state Potts model on the tripartite reo net, consisting of corner-sharing regular octahedrons, confirm this counterintuitive prediction while showcasing switching self-assembly upon an ordering phase transition. The possible inequivalence of three directions, i.e., more symmetry breaking than uniaxiality, is found and discussed for the ordered phase of this model at finite temperatures. Some additional analyses of the model are provided, including the possibility of a metastable isotropic order, which aligns better with intuition.