We take inspiration from the early Rubik’s cube to design an analogous mechano-responsive system. We focus on polymer-grafted nanoparticles (PGNs), where each rigid nanoparticle core is decorated with a corona of polymer chains. The free ends of these chains encompass reactive functional groups that allow the polymers to form “arms” between neighboring particles and thus, interconnect the PGNs into a network. In effect, these polymer arms act as the elastic bands and the nanoparticles correspond to the individual blocks in the toy. Using computational modeling, we show that by applying torsion to this material, we can achieve significant control over the arrangement of a binary mixture of nanoparticles and hence, tailor the nanostructure of the composite.