Figure 3. The generic topological system.

(a) The equilibrium configuration of a self-assembled periodic array of rigid dimers with inversion symmetry relative to their centre of mass (marked by the dot). One important observation is that, regardless of the details of the self-assembly process, the periodic array, as a whole, has the inversion symmetry. (b) A dynamical configuration of the dimer chain showing the relevant degrees of freedom that are the translations of the dimer centres along the axis of the chain and the rotation of the dimers. It also shows how the degrees of freedom transform under the inversion operation. The key observation here is that the translational degrees of freedom change sign while the rotational ones do not.