In this paper, we use Grazing-Incidence X-ray Diffraction (GIXRD) to determine the atomic structure of the Si-rich 3C-SiC(001)3x2 surface reconstruction. Up to 5 models have been proposed in the past for this surface reconstruction, based on structural and non-structural experimental techniques and theoretical calculations. Until now, no clear evidence for a unique model had been given. Our GIXRD experiments allow to exclude all models except one. The results are in qualitative agreement with the Two Asymmetric Adlayer Dimer (TAAD) model proposed on the basis of ab-initio calculations: the reconstruction is made of 3 Si planes, the topmost layer consisting of Si-Si dimer rows with the dimers being perpendicular to the rows. However the data also reveal significant differences in atomic positions with the TAAD model. In particular we find alternately long and short Si dimers (ALSD) in the second reconstructed plane leading to the tilt of the topmost Si dimers. This further explains why the dimers are all tilted in the same direction with no buckling (i-e not anticorrelated) contrary to the Si or Ge (001) surfaces.