Let $f$ be a piecewise affine concave function with $\Lambda={\operatorname{dom}}(f)$ and $\Lambda^{\prime}=\operatorname{stab}(f)$. Then $\Pi(f)$ and $\Pi(f^{\vee})$ are polyhedral complexes in $\Lambda$ and $\Lambda^{\prime}$ respectively. Moreover, they are dual of each other. In particular, the vertices of $\Pi(f)$ are in bijection with the polyhedra of $\Pi(f^{\vee})$ of maximal dimension.