With an estimated diameter in the 320 to 350km 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>400km (Ceres, Vesta, Pallas and Hygiea) and the numerous smaller bodies with diameter 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<=200km) 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+/-6km implies a bulk density of {rho}=1.98+/-0.68g/cm^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<=300km) less massive (m<=3x10^19^kg) bodies.

Cone search capability for table J/A+A/633/A65/tablea1 (List of VLT/SPHERE disk-resolved images obtained in the I filter by the ZIMPOL camera)