Accurate shape description is a challenge in material science. Small-angle X-ray scattering (SAXS) can provide the shape, size and polydispersity of nanoparticles by form factor modeling. However, simple geometrical models such as the ellipsoid may not be enough to describe objects with complex shapes. In this work we show that the form factor of gold nanobipyramids is accurately described by a truncated bicone model, which is validated by comparison with transmission electron microscopy (TEM) data for nine different synthesis batches: we obtain the average shape parameters (width, height, and truncation) and the sample polydispersity. In contrast, the ellipsoid model yields worse fits of the SAXS data and exhibits systematic discrepancies with the TEM results.