A single grain of a modulated icosahedral AlCuFe phase has been studie
d by X-ray diffraction using the synchrotron light source at LURE (Lab
oratoire pour l'Utilisation du Rayonnement Electromagnetique, Orsay, F
rance), Each main icosahedral reflection is flanked by twelve satellit
es along fivefold directions. The integrated intensity of 22 reflectio
ns and of their satellites have been measured in a broad G(parallel-to
) and G(perpendicular-to) range. Despite the presence of the satellite
s the overall icosahedral symmetry is maintained. The results are inte
rpreted on the basis of six independent displacive cosine waves, propa
gating along the fivefold axes of the 6-dim periodic space. The polari
zation of these cosine waves is found to be longitudinal with a main c
omponent in perpendicular space which means that the modulation is of
<<phason>> origin.