Let be the distance from a compact set in the space of matrices. This note determines the set of zeroes of the polyconvex hull of where It is shown that the set-valued function is constant on the intervals where while at the set generally jumps down discontinuously. The values at the beginnings of intervals of constancy are characterized as -polyconvex hulls of to be defined below, where is the convex hull and the standard polyconvex hull. As an illustration, are evaluated for all if and for arbitrary if and/or In the remaining cases only bounds are obtained. A surprising consequence is that the quasiconvex hull of is not polyconvex if </p>