The surfaces of quasiperiodic materials hold tremendous interest due to their potential for creating new forms of matter with exotic properties. The use of quasicrystalline surfaces as templates for adsorbed monolayers provides the opportunity to transfer typical quasicrystalline properties to a wide range of materials. We demonstrate this approach by exposing a colloidal monolayer to a decagonal laser light field where the substrate strength is continuously adjustable. At intermediate substrate potentials we observe a novel pseudomorphic phase exhibiting likewise crystalline and quasicrystalline order and which can be explained by an Archimedean-like tiling structure. In addition to this surprising new link between such tilings and quasicrystals our experiments allow to investigate in real space how single-element monolayers arrange locally on quasicrystalline surfaces.