All Polyhedra and Polytopes

This group gathers theorems about polyhedra and their higher-dimensional generalizations, polytopes, the solid figures bounded by flat faces. It covers Euler's polyhedron formula relating a polyhedron's vertices, edges, and faces, Cauchy's rigidity theorem showing that a convex polyhedron's shape is determined by its faces, Alexandrov's existence and uniqueness theorem for polyhedra with prescribed curvature, and further three-dimensional analogues of planar results, including De Gua's theorem generalizing the Pythagorean theorem to a tetrahedron and Commandino's theorem on where a tetrahedron's medians meet.