We report STM investigations on a linear oligophenyleneethylene (OPE)-based self-assembling Pd(II) complex 1 that forms highly-ordered concentration dependent patterns on HOPG. At high concentration, 2D lamellar structures are observed whereas the dilution of the system below a critical concentration leads to the formation of visually attractive rhombitrihexagonal Archimedean tiling arrangements featuring three different kinds of polygons: triangles, hexagons and rhombi. The key participation of the Cl ligands attached to the Pd(II) centre in multiple C–H⋯Cl interactions was demonstrated by comparing the patterns of 1 with those of an analogous non-metallic system 2.