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About: Steinitz's theorem     Goto   Sponge   NotDistinct   Permalink

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Type: yago:WikicatTheoremsInDiscreteGeometryyago:WikicatTheoremsInGraphTheoryyago:Abstraction100002137yago:Communication100033020yago:Graph107000195yago:Message106598915yago:Proposition106750804yago:Statement106722453yago:Theorem106752293yago:VisualCommunication106873252yago:WikicatPlanarGraphs New Facet based on Instances of this Class

In polyhedral combinatorics, a branch of mathematics, Steinitz's theorem is a characterization of the undirected graphs formed by the edges and vertices of three-dimensional convex polyhedra: they are exactly the 3-vertex-connected planar graphs. That is, every convex polyhedron forms a 3-connected planar graph, and every 3-connected planar graph can be represented as the graph of a convex polyhedron. For this reason, the 3-connected planar graphs are also known as polyhedral graphs.