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We show that model molecules with particular rotational symmetries canself-assemble into network structures equivalent to rhombus tilings. Thisassembly happens in an emergent way, in the sense that molecules spontaneouslyselect irregular 4-fold local coordination from a larger set of possible localbinding geometries. The existence of such networks can be rationalized bysimple geometrical arguments, but the same arguments do not guarantee networks'spontaneous self-assembly. This class of structures must in certain regimes ofparameter space be able to reconfigure into networks equivalent to triangulartilings.

Emergent rhombus tilings from molecular interactions with $M$-fold rotational symmetry