CRYSTALLOGRAPHY OF ICOSAHEDRAL CRYSTALS

Abstract
The crystallography of icosahedral crystals is constructed. The actual three-dimensional crystal is represented by a three-dimensional cut in a regular six-dimensional periodic crystal with symmetry described by a six-dimensional space group, and the positions of atoms correspond to an arrangement of hypersurface segments. The resulting crystal can not in general be viewed as a space-filling arrangement of a small number of different "Penrose tiles." The intensities of Bragg spots are given directly as the intensities of Bragg spots of the six-dimensional crystal.