Quasicrystal surfaces: structure and potential as templates

We present a review of recent progress in determining the surface structure of quasicrystals, with emphasis on their connections to mathematical tiling models. The review focusses in particular on the five-fold surface of icosahedral Al-Pd-Mn and the ten-fold surface of decagonal AI-Ni-Co. We also assess their potential as templates for the formation of two-dimensional quasicrystalline overlayers with reference to recent investigations of atomic and molecular adsorption.