Abstract
Classical H. Minkowski theorems on existence and uniqueness of convex polyhedra with prescribed directions and areas of faces as well as the well-known generalization of H. Minkowski uniqueness theorem due to A.D. Alexandrov are extended to a class of nonconvex polyhedra which are called polyhedral herissons and may be described as polyhedra with injective spherical image.
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Alexandrov, V. Minkowski-type and Alexandrov-Type Theorems for Polyhedral Herissons. Geometriae Dedicata 107, 169–186 (2004). https://doi.org/10.1007/s10711-004-4090-3
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DOI: https://doi.org/10.1007/s10711-004-4090-3