Abstract
By using new decoration for the two-dimensional Penrose tiling, we construct a τ 4-scaling three-dimensional icosahedral structure consisting of three types of zonohedra; a triacontahedron, a star-like sixty-face rhombohedron and a rhombic icosahedron. The present 3D model extends only in a layer perpendicular to the five-fold axis of icosahedral symmetry with a finite thickness along the axis and there are few overlaps between the zonohedra. We calculate the electron diffraction pattern for the present model by putting atoms at all the vertices of the three types of zonohedral units. Reasonable agreement with the experimental results for i-AlMn phase is obtained.
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