We propose a tiling-and-decoration model of the icosahedral phase of Al-Mn-Si, in which a 126-atom ‘‘double’’ Mackay icosahedron and a 54-atom ‘‘simple’’ Mackay icosahedron alternate on the even and odd nodes of the tiling of four canonical cells. The model structure exhibits weak six-dimensional fcc ordering introduced by Al-vacancy alternation, similar to that observed in the related α phase. The density of the model is consistent with experimental data and calculation of the x-ray- and neutron-diffraction intensities leads to good agreement with experimental data in both cases: R factors are 0.09 and 0.16, respectively.

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