Xe adsorption on the (100) surface of the complex alloy Al 13Co4 has been carried out using low-energy electron diffraction (LEED) and grand canonical Monte Carlo (GCMC) simulations. This surface is an approximant to the 10-fold surface of decagonal Al-Ni-Co, on which Xe adsorption has been studied previously. The adsorption behavior on the periodic surface is largely similar to that on the quasicrystal (layer-by-layer growth, hexagonal ordering near the onset of the second-layer adsorption), but it also has some differences, such as the complete lack of registry of the Xe layer with the substrate structure in the hexagonal phase, and a high sensitivity of the Xe epitaxial direction to trace impurities. In the simulations, an ordering transition was observed between the low-density and high-density monolayer regimes that involves a uniaxial compression of the monolayer film. © 2011 American Physical Society.