  We present a general construction of hypersurfaces with vanishing hessian,
starting from any irreducible non-degenerate variety whose dual variety is a
hypersurface and based on the so called Dual Cayley Trick. The geometrical
properties of these hypersurfaces are different from the known series
constructed until now. In particular, their dual varieties can have arbitrary
codimension in the image of the associated polar map.
