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High Quality Content by WIKIPEDIA articles! Cauchy's theorem is a theorem in geometry, named after Augustin Cauchy. It states that convex polytopes in three dimensions with congruent corresponding faces must be congruent to each other. That is, any polyhedral net formed by unfolding the faces of the polyhedron onto a flat surface, together with gluing instructions describing which faces should be connected to each other, uniquely determines the shape of the original polyhedron. For instance, if six squares are connected together in the pattern of a cube, then they must form a cube: there is no convex polyhedron with six square faces connected in the same way that does not have the same shape.