A six-dimensional cluster model of icosahedral Al-Pd-Mn (i-Al-Pd-Mn) quasicrystals used in the recent structure refinement is described in detail. This model is based on five kinds of clusters located at vertices, edge centers of the inflated three-dimensional Penrose pattern (3DPP) with an edge length of about 20 {}, and two body-diagonal positions of each acute rhombohedron. Two kinds of 20 {} clusters, one of which is seen in β-Al-Pd-Mn-Si, are located at even- and odd-parity 12-fold vertices of the inflated 3DPP. This is proved to give small R factors (Rw=0.055,R=0.049) for 493 independent reflections and leads to the 1/1 and 2/1 approximant structures of i-Al-Pd-Mn (α- and β-Al-Pd-Mn-Si) by introducing appropriate cubic phason strains and taking a three-dimensional cut.
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Yamamoto et al. (2003) studied this question.