Emergent rhombus tilings from molecular interactions with $M$-fold   rotational symmetry
  We show that model molecules with particular rotational symmetries can self-assemble into network structures equivalent to rhombus tilings. This assembly happens in an emergent way, in the sense that molecules spontaneously select irregular 4-fold local coordination from a larger set of possible local binding geometries. The existence of such networks can be rationalized by simple geometrical arguments, but the same arguments do not guarantee networks' spontaneous self-assembly. This class of structures must in certain regimes of parameter space be able to reconfigure into networks equivalent to triangular tilings. 
Stephen Whitelam, Isaac Tamblyn, Juan P. Garrahan, Peter H. Beton
cond-mat.stat-mech cond-mat.soft