  Context. The high-angular-resolution capability of the new-generation
ground-based adaptive-optics camera SPHERE at ESO VLT allows us to assess, for
the very first time, the cratering record of medium-sized (D~100-200 km)
asteroids from the ground, opening the prospect of a new era of investigation
of the asteroid belt's collisional history. Aims. We investigate here the
collisional history of asteroid (6) Hebe and challenge the idea that Hebe may
be the parent body of ordinary H chondrites, the most common type of meteorites
found on Earth (~34% of the falls). Methods. We observed Hebe with SPHERE as
part of the science verification of the instrument. Combined with earlier
adaptive-optics images and optical light curves, we model the spin and
three-dimensional (3D) shape of Hebe and check the consistency of the derived
model against available stellar occultations and thermal measurements. Results.
Our 3D shape model fits the images with sub-pixel residuals and the light
curves to 0.02 mag. The rotation period (7.274 47 h), spin (343 deg,+47 deg),
and volume-equivalent diameter (193 +/- 6km) are consistent with previous
determinations and thermophysical modeling. Hebe's inferred density is 3.48 +/-
0.64 g.cm-3 , in agreement with an intact interior based on its H-chondrite
composition. Using the 3D shape model to derive the volume of the largest
depression (likely impact crater), it appears that the latter is significantly
smaller than the total volume of close-by S-type H-chondrite-like asteroid
families. Conclusions. Our results imply that (6) Hebe is not the most likely
source of H chondrites. Over the coming years, our team will collect similar
high-precision shape measurements with VLT/SPHERE for ~40 asteroids covering
the main compositional classes, thus providing an unprecedented dataset to
investigate the origin and collisional evolution of the asteroid belt.
