We report on structural investigations on multi-fold stacks of InGaAs quantum dots (QDs) embedded within a GaAs matrix. The structures have been grown by means of metalorganic chemical vapor deposition. Cross-sectional transmission electron micrographs prove a pronounced vertical QD correlation, while plan-view images do not show any lateral ordering. Grazing incidence diffraction within various crystallographic zones clearly reveal a QD shape with a four-fold symmetry. Comparing dynamical scattering simulations, which base on finite element calculations for the strain field show that the shape of the QDs can be described by a prism with a flat top on a thin wetting layer. The mean lateral dot distance evaluated from diffuse X-ray scattering agrees well with the QD density estimated from TEM plan-view images.