  In this work, we investigate the equilibrium figures of a dumb-bell-shaped
sequence with which we are still not well acquainted. Studies have shown that
these elongated and nonconvex figures may realistically replace the classic
"Roche binary approximation" for modeling putative peanut-shaped or contact
binary asteroids. The best-fit dumb-bell shapes, combined with the known
rotational period of the objects, provide estimates of the bulk density of
these objects. This new class of mathematical figures has been successfully
tested on the observed light curves of three noteworthy small bodies: main-belt
asteroid 216 Kleopatra, Trojan asteroid 624 Hektor and Edgeworth-Kuiper-belt
object 2001 QG298. Using the direct observations of Kleopatra and Hektor
obtained with high spatial resolution techniques and fitting the size of the
dumb-bell-shaped solutions, we derived new physical characteristics in terms of
equivalent radius and bulk density. In particular, the growing inadequacy of
the radar shape model for interpreting any type of observations of Kleopatra
(light curves, AO images, stellar occultations) in a satisfactory manner
suggests that Kleopatra is more likely to be a dumb-bell-shaped object than a
"dog-bone".
