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The realization of complex long-range ordered structures in a Euclidean plane presents a significant challenge en route to the utilization of their unique physical and chemical properties. Recent progress in on-surface supramolecular chemistry has enabled the engineering of regular and semi-regular tilings, expressing translation symmetric, quasicrystalline, and fractal geometries. However, the  k -uniform tilings possessing several distinct vertices remain largely unexplored. Here, we show that these complex geometries can be prepared from a simple bitopic molecular precursor – 4,4’-biphenyl dicarboxylic acid (BDA) – by its controlled chemical transformation on the Ag(001) surface. The realization of 2- and 3-uniform tilings is enabled by partially carboxylated BDA mediating the seamless connection of two distinct binding motifs in a single long-range ordered molecular phase. These results define the basic self-assembly criteria, opening way to the utilization of complex supramolecular tilings.

Complex k-uniform tilings by a simple bitopic precursor self-assembled on Ag(001) surface