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It is shown that tiling in icosahedral quasicrystals can also be properlydescribed by cyclic twinning at the unit cell level. The twinning operation isapplied on the primitive prolate golden rhombohedra, which can be considered aresult of a distorted face-centered cubic parent structure. The shape of therhombohedra is determined by an exact space filling, resembling the forbiddenfive-fold rotational symmetry. Stacking of clusters, formed around multiplytwinned rhombic hexecontahedra, keeps the rhombohedra of adjacent clusters indiscrete relationships. Thus periodicities, interrelated as members of aFibonacci series, are formed. The intergrown twins form no obvious twinboundaries and fill the space in combination with the oblate goldenrhombohedra, formed between clusters in contact. Simulated diffraction patternsof the multiply twinned rhombohedra and the Fourier transform of an extendedmodel structure are in full accord with the experimental diffraction patternsand can be indexed by means of three-dimensional crystallography.

The Equivalence Between Unit-Cell Twinning and Tiling in Icosahedral Quasicrystals