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A well-known result in the study of convex polyhedra, due to Minkowski, isthat a convex polyhedron is uniquely determined (up to translation) by thedirections and areas of its faces. The theorem guarantees existence of thepolyhedron associated to given face normals and areas, but does not provide aconstructive way to find it explicitly. This article provides an algorithm toreconstruct 3D convex polyhedra from their face normals and areas, based on anmethod by Lasserre to compute the volume of a convex polyhedron in$\mathbb{R}^n$. A Python implementation of the algorithm is available athttps://github.com/gsellaroli/polyhedrec.

An algorithm to reconstruct convex polyhedra from their face normals and areas