It is shown that tiling in icosahedral quasicrystals can also be properly
described by cyclic twinning at the unit cell level. The twinning operation is
applied on the primitive prolate golden rhombohedra, which can be considered a
result of a distorted face-centered cubic parent structure. The shape of the
rhombohedra is determined by an exact space filling, resembling the forbidden
five-fold rotational symmetry. Stacking of clusters, formed around multiply
twinned rhombic hexecontahedra, keeps the rhombohedra of adjacent clusters in
discrete relationships. Thus periodicities, interrelated as members of a
Fibonacci series, are formed. The intergrown twins form no obvious twin
boundaries and fill the space in combination with the oblate golden
rhombohedra, formed between clusters in contact. Simulated diffraction patterns
of the multiply twinned rhombohedra and the Fourier transform of an extended
model structure are in full accord with the experimental diffraction patterns
and can be indexed by means of three-dimensional crystallography
