Asteroid (16) Psyche is the target of the NASA Psyche mission. It is considered as one of the few main-belt bodies that could be an exposed proto-planetary metallic core and that would thus be related to iron meteorites. Such association is however challenged by both its near- and mid-infrared spectral properties (e.g. Hardersen et al. Icarus 175, 2005; Takir et al. AJ, 153, 2017; Landsman et al. Icarus, 304, 2018). We observed (16) Psyche with ESO VLT SPHERE/ZIMPOL as part of our large program (ID 199.C-0074, PI Vernazza) between April 24 and June 6 2018. We use the high-angular resolution of these observations to reconstruct the 3D shape model of Psyche. When combined with the most recent estimates of its mass, the volume that we derive led to a bulk density of 3.99 ± 0.26 g.cm<SUP>-3</SUP> for Psyche. While such density is incompatible at the 3-sigma level with any iron meteorites (&#732;7.8 g.cm<SUP>-3</SUP>), it appears fully consistent with that of stony-iron meteorites such as mesosiderites (density &#732;4.25 g.cm<SUP>-3</SUP>). Although our observations only covered the northern hemisphere of Psyche, they reveal the presence of two peculiar units in the front views, namely one low and one high brightness regions nicknamed Panthia and Meroe. Meroe unit is about 7% brighter than the surrounding region, whereas the Panthia unit is 8% fainter. Panthia is a depression with a width of 90 km and a depth of 10 km. We did not detect any moons around Psyche and estimate the minimum radius of a moon to be detected around Psyche to 730 ± 100 m at 150 km (so 0.2% x R<SUB>Hill</SUB>) of the primary and 400 ± 100 m at 2000 km from the primary corresponding to 3% x R<SUB>Hill</SUB>) where most of the satellites of >100-km asteroids have been seen so far (Yang et al. AJL 820:L35, 2016). Considering that the visible and near-infrared spectral properties of mesosiderites are similar to those of Psyche, there is merit to the initial hypothesis by Davis et al. (1999) that Psyche could be a plausible candidate parent body for mesosiderites (Viikinkoski et al. submitted to A&A, 2018). This material is based upon work partially supported by the National Science Foundation under Grant No 1743015.