Same as Figs. 4 (top) and 2 (bottom) but without error bars and with asteroid numbers. See Vernazza et al. (2021, Table 1) for the correspondences between numbers and asteroid names. The bottom panel shows a zoomed-in view of the x-axis to exclude the red point that corresponds to (216) Kleopatra, which has already been identified as a dumbbell body (Ostro et al. 2000). The asteroids closest to a Maclaurin ellipsoid are in blue, and those closest to a Jacobi ellipsoid are in red. This shows that the projections formed by these two figures can be misleading with respect to a 3D misfit. In the bottom panel, we have hatched the surface that corresponds to possible Clairaut ellipsoids (see Sect. 3.3).