Title: An algorithm to reconstruct convex polyhedra from their face normals and areas,
Abstract: A well-known result in the study of convex polyhedra, due to Minkowski, is
that a convex polyhedron is uniquely determined (up to translation) by the
directions and areas of its faces. The theorem guarantees existence of the
polyhedron associated to given face normals and areas, but does not provide a
constructive way to find it explicitly. This article provides an algorithm to
reconstruct 3D convex polyhedra from their face normals and areas, based on an
method by Lasserre to compute the volume of a convex polyhedron in
$\mathbb{R}^n$. A Python implementation of the algorithm is available at
this https URL.