Abstract
Analytical formulations of icosahedral quasi-crystal structure treated as the projection from a six-dimensional hypercubic crystal and its Fourier transform have been derived with a three-dimensional orthogonal coordinate system. Each coordinate axis consists of two basic lengths related to each other by a multiplier equal to the golden ratio. The relationship between icosahedral and orthogonal coordinates in both real and reciprocal spaces is demonstrated. The expression obtained for the icosahedral structure is identical with the density-wave description.
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