  With an estimated diameter in the 320 to 350 km range, (704) Interamnia is
the fifth largest main belt asteroid and one of the few bodies that fills the
gap in size between the four largest bodies with $D$ > 400 km (Ceres, Vesta,
Pallas and Hygiea) and the numerous smaller bodies with $D$ $\lesssim$ 200 km.
However, despite its large size, little is known about the shape and spin state
of Interamnia and, therefore, about its bulk composition and past collisional
evolution. We aimed to test at what size and mass the shape of a small body
departs from a nearly ellipsoidal equilibrium shape (as observed in the case of
the four largest asteroids) to an irregular shape as routinely observed in the
case of smaller ($D$ $\lesssim$ 200 km) bodies. We observed Interamnia as part
of our ESO VLT/SPHERE large program (ID: 199.C-0074) at thirteen different
epochs. In addition, several new optical lightcurves were recorded. These data,
along with stellar occultation data from the literature, were fed to the
All-Data Asteroid Modeling (ADAM) algorithm to reconstruct the 3D-shape model
of Interamnia and to determine its spin state. Interamnia's volume-equivalent
diameter of 332 $\pm$ 6 km implies a bulk density of $\rho$=1.98 $\pm$ 0.68
gcm$^{-3}$ , which suggests that Interamnia - like Ceres and Hygiea - contains
a high fraction of water ice, consistent with the paucity of apparent craters.
Our observations reveal a shape that can be well approximated by an ellipsoid,
and that is compatible with a fluid hydrostatic equilibrium at the 2 $\sigma$
level. The rather regular shape of Interamnia implies that the size and mass
limit, under which the shapes of minor bodies with a high amount of water ice
in the subsurface become irregular, has to be searched among smaller ($D$
$\lesssim$ 300km) less massive ($m$ $\lesssim$ 3x10$^{19}$ kg) bodies.
