Self-consistent spin-polarized electronic-structure calculations are carried out on a supercell of a 54-atom Mackay icosahedron used to simulate a ${\mathrm{Al}}_{78}$${\mathrm{Mn}}_{22}$ quasicrystal. When the 12 Mn atoms are placed at the corners of the inner icosahedron, they do not develop any magnetic moment. When they are placed at the corners of the outer icosahedron, the magnetic moment per manganese atom is 1.39${\mathrm{\mu }}_{\mathit{B}}$, which is in very good agreement with the experimental data for this composition.

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