We have investigated, by means of X-ray diffraction reciprocal space mapping and X-ray reflectivity, multilayers of self-organized InGaAs quantum dots grown on GaAs by MBE. An anisotropy of the average inter-dot spacings in the [100] and [110] directions was found, consistent with an ordering of the dots in a two-dimensional square lattice with main axes along the <100>-directions and a lattice parameter of 55 nm. The nearly perfect vertical alignment (stacking) of the dots was deduced consistently from the diffraction peak shape and from measurements of the resonant diffuse scattering in the X-ray reflection regime.