We show that friction anisotropy is an intrinsic property of the atomic structure of Al–Ni–Co decagonal quasicrystals and not only of clean and well-ordered surfaces that can be prepared in vacuum [J.Y. Park et al., Science309, 1354 (2005)]. Friction anisotropy is manifested in both nanometer-size contacts obtained with sharp atomic force microscope tips and macroscopic contacts produced in pin-on-disk tribometers. We show that the friction anisotropy, which is not observed when an amorphous oxide film covers the surface, is recovered when the film is removed due to wear. Equally important is the loss of the friction anisotropy when the quasicrystalline order is destroyed due to cumulative wear. These results reveal the intimate connection between the mechanical properties of these materials and their peculiar atomic structure.