The atomic structure of the perfect AlPdMn icosahedral phase has been studied on a single grain by anomalous X-ray diffraction close to the Pd edge. A method is proposed for relative normalization of the data, in order to extract the partial structure factor F_Pd of the Pd atoms. The Pd is found to be very ordered in the six-dimensional description of the quasicrystal, as was previously inferred from X-ray and neutron single-crystal diffraction data. However, a phason Debye-Waller-like term has to be introduced to account for the data. Comparison of the present data set with low-resolution data indicates the existence of diffuse scattering located close to the Bragg reflections whose intensity scales as (1-exp(-B_perpQ²_perp)) as expected from random fluctuations of the atomic surfaces. The average fluctuation is found to be of the order of 1 AA. Moreover the comparison of the data with a spherical model shows that the atomic surface describing Pd atoms is likely to be made of several disjointed pieces.