  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.
