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Using electron diffraction, we show that free electron metals such as sodium and potassium form a highly regular quasiperiodic monolayer on the fivefold surface of icosahedral Al-Pd-Mn and that the quasiperiodicity propagates up to the second layer in sodium. Our photoelectron spectroscopy results show that the quasicrystalline alkali metal adlayer does not exhibit a pseudogap near the Fermi level, thought to be charactersitic for the electronic structure of quasicrystalline materials. Calculations based on density functional theory provide a model structure for the quasicrystalline alkali metal monolayer and confirm the absence of a pseudogap.