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We show that the structures of cubic Cd6Yb and Cd6Ca crystals are closely related to those of recently found stable icosahedral Cd-Yb and Cd-Ca alloys. These structures are described as a periodic packing of rhombohedra having different atomic decoration in terms of three-dimensional Penrose tiling. A new type of icosahedral cluster composed of 66 atoms is found. The innermost shell of the cluster consisting of four Cd atoms breaks its entire icosahedral symmetry.
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Takakura et al. (2001) studied this question.
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