V. Elser in reference  stated that the Katz and Gratias model [2,3] of icosahedral Al–Cu–Fe and the Boudard and de Boissieu model [4,5] of icosahedral Al–Pd–Mn can both be explained as a decoration of the primitive icosahedral tiling P  by the Bergman and therefore automatically by Mackay polyhedra. Elser introduced in  a unifying model that is partly deterministic and partly probabilistic, i.e. some atomic positions are fixed and another occupied with certain probabilities. Z. Papadopolos introduced an analogous unifying model as a decoration by Bergman polyhedra of an F-phase tiling *(2F) [7,8], using the fact that the tiling P is locally derivable from the tiling *(2F) . She constructed the windows in  for the unifying model formulated in . The Papadopolos and Kasner model [9,10] is a deterministic model with polyhedral windows, somewhat different from the Katz and Gratias windows.
 V. Elser
Phil. Mag. B, 1996, 73, 641.
 A. Katz and D. Gratias J. Non-Cryst. Solid, 1993, 153&154, 187.
 A. Katz and D. Gratias in Proceedings of the 5th International Conference on Quasicrystals, Ed. by C. Janot and R. Mosseri, World Scientific, Singapore, 1995, 164.
 M. Boudard, M. de Boissieu, C. Janot, G. Heger, C. Beeli, H.-U. Nissen, H. Vincent, R. Ibberson, M. Audier and J. M. Dubois J. Phys.: Condens. Matter, 1992, 4, 10149.
 M. de Boissieu, P. Stephens, M. Boudard, C. Janot, D. L. Chapman and M. Audier J. Phys.:Condens. Matter, 1994, 6, 10725.
 P. Kramer and R. Neri Acta Cryst. A, 1984, 40, 580.
 P. Kramer, Z. Papadopolos and D. Zeidler in Symmetries in Science V: Algebraic Structures, their Representions, Realizations and Physical Applications, Ed. by B. Gruber, L. C. Biedenharn and H. D. Döbner, Plenum Press, New York, 1991, 395.
 Z. Papadopolos, P. Kramer and W. Liebermeister in Aperiodic '97, Ed. by M. de Boissieu, J.-L. Verger-Gaugry and R. Currat, World Scientific, Singapore, 1998, 173.
 G. Kasner, Z. Papadopolos, P. Kramer and D. E. Bürgler Phys. Rev. B, 1999, 60, 3899.
 Z. Papadopolos, P. Kramer, G. Kasner and D. E. Bürgler Mat. Res. Soc. Symp., 1999, 553, 231.
The shortest interatomic distances in the model, along the 5-fold, 2-fold and 3-fold axes are τ-1, τ-1 and τ-1, respectively. The standard distances , , and are related by /√3 = /(τ+2)1/2 = /2, where τ = (1 + √5)/2. The standard distance = 1 / √2 in E|| is set to be 4.561 Å for i-Al–Pd–Mn and 4.465 Å for i-Al–Cu–Fe.
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