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- Steinitz's_theorem abstract "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. Steinitz's theorem is named after Ernst Steinitz, who proved it in 1922. Branko Grünbaum has called this theorem “the most important and deepest known result on 3-polytopes.”The name "Steinitz's theorem" has also been applied to other results of Steinitz: the Steinitz exchange lemma implying that each basis of a vector space has the same number of vectors, the theorem that if the convex hull of a point set contains a unit sphere, then the convex hull of a finite subset of the point contains a smaller concentric sphere, and Steinitz's vectorial generalization of the Riemann series theorem on the rearrangements of conditionally convergent series.↑ ↑ 2.0 2.1 ↑ ↑ ↑ ↑ ↑ ↑ ↑ ↑".
- Steinitz's_theorem thumbnail Schegel_diagram_as_shadow.png?width=300.
- Steinitz's_theorem wikiPageID "19762817".
- Steinitz's_theorem wikiPageRevisionID "569917909".
- Steinitz's_theorem hasPhotoCollection Steinitz's_theorem.
- Steinitz's_theorem subject Category:Geometric_graph_theory.
- Steinitz's_theorem subject Category:Planar_graphs.
- Steinitz's_theorem subject Category:Polyhedral_combinatorics.
- Steinitz's_theorem subject Category:Theorems_in_discrete_geometry.
- Steinitz's_theorem subject Category:Theorems_in_graph_theory.
- Steinitz's_theorem type Abstraction100002137.
- Steinitz's_theorem type Communication100033020.
- Steinitz's_theorem type Graph107000195.
- Steinitz's_theorem type Message106598915.
- Steinitz's_theorem type PlanarGraphs.
- Steinitz's_theorem type Proposition106750804.
- Steinitz's_theorem type Statement106722453.
- Steinitz's_theorem type Theorem106752293.
- Steinitz's_theorem type TheoremsInCombinatorics.
- Steinitz's_theorem type TheoremsInGraphTheory.
- Steinitz's_theorem type VisualCommunication106873252.
- Steinitz's_theorem comment "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.".
- Steinitz's_theorem label "Steinitz's theorem".
- Steinitz's_theorem sameAs m.080fdkh.
- Steinitz's_theorem sameAs Q7606897.
- Steinitz's_theorem sameAs Q7606897.
- Steinitz's_theorem sameAs Steinitz's_theorem.
- Steinitz's_theorem wasDerivedFrom Steinitz's_theorem?oldid=569917909.
- Steinitz's_theorem depiction Schegel_diagram_as_shadow.png.
- Steinitz's_theorem isPrimaryTopicOf Steinitz's_theorem.
