Matches in DBpedia 2015-10 for { <http://dbpedia.org/resource/Steinitzs_theorem> ?p ?o }
- Steinitzs_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 (simple) 3-vertex-connected planar graphs (with at least four vertices). 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 submitted its first proof for publication in 1916. 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 ↑ ↑ ↑ ↑ ↑ ↑ ↑ ↑".
- Steinitzs_theorem thumbnail Schegel_diagram_as_shadow.png?width=300.
- Steinitzs_theorem wikiPageID "19762817".
- Steinitzs_theorem wikiPageLength "32254".
- Steinitzs_theorem wikiPageOutDegree "89".
- Steinitzs_theorem wikiPageRevisionID "683360946".
- Steinitzs_theorem wikiPageWikiLink 3-polytope.
- Steinitzs_theorem wikiPageWikiLink Apollonian_network.
- Steinitzs_theorem wikiPageWikiLink Balinskis_theorem.
- Steinitzs_theorem wikiPageWikiLink Branko_Grünbaum.
- Steinitzs_theorem wikiPageWikiLink Category:Geometric_graph_theory.
- Steinitzs_theorem wikiPageWikiLink Category:Planar_graphs.
- Steinitzs_theorem wikiPageWikiLink Category:Polyhedral_combinatorics.
- Steinitzs_theorem wikiPageWikiLink Category:Theorems_in_discrete_geometry.
- Steinitzs_theorem wikiPageWikiLink Category:Theorems_in_graph_theory.
- Steinitzs_theorem wikiPageWikiLink Circle_packing_theorem.
- Steinitzs_theorem wikiPageWikiLink Circumscribed_sphere.
- Steinitzs_theorem wikiPageWikiLink Circumsphere.
- Steinitzs_theorem wikiPageWikiLink Colin_de_Verdière_graph_invariant.
- Steinitzs_theorem wikiPageWikiLink Complete_(complexity).
- Steinitzs_theorem wikiPageWikiLink Complete_graph.
- Steinitzs_theorem wikiPageWikiLink Conditional_convergence.
- Steinitzs_theorem wikiPageWikiLink Convex_body.
- Steinitzs_theorem wikiPageWikiLink Convex_hull.
- Steinitzs_theorem wikiPageWikiLink Convex_polyhedron.
- Steinitzs_theorem wikiPageWikiLink Convex_polytope.
- Steinitzs_theorem wikiPageWikiLink Convex_position.
- Steinitzs_theorem wikiPageWikiLink Császár_polyhedron.
- Steinitzs_theorem wikiPageWikiLink Cycle_(graph_theory).
- Steinitzs_theorem wikiPageWikiLink Double_exponential_function.
- Steinitzs_theorem wikiPageWikiLink Dual_graph.
- Steinitzs_theorem wikiPageWikiLink Dual_polyhedron.
- Steinitzs_theorem wikiPageWikiLink Edge_(graph_theory).
- Steinitzs_theorem wikiPageWikiLink Ernst_Steinitz.
- Steinitzs_theorem wikiPageWikiLink Euclidean_plane.
- Steinitzs_theorem wikiPageWikiLink Existential_theory_of_the_reals.
- Steinitzs_theorem wikiPageWikiLink Fxc3xa1rys_theorem.
- Steinitzs_theorem wikiPageWikiLink Graph_(mathematics).
- Steinitzs_theorem wikiPageWikiLink Graph_automorphism.
- Steinitzs_theorem wikiPageWikiLink Graph_drawing.
- Steinitzs_theorem wikiPageWikiLink Graph_minor.
- Steinitzs_theorem wikiPageWikiLink Grid_graph.
- Steinitzs_theorem wikiPageWikiLink Halin_graph.
- Steinitzs_theorem wikiPageWikiLink Homography.
- Steinitzs_theorem wikiPageWikiLink Inscribed_sphere.
- Steinitzs_theorem wikiPageWikiLink Insphere.
- Steinitzs_theorem wikiPageWikiLink K-vertex-connected_graph.
- Steinitzs_theorem wikiPageWikiLink Lattice_(order).
- Steinitzs_theorem wikiPageWikiLink Lattice_graph.
- Steinitzs_theorem wikiPageWikiLink Line_segment.
- Steinitzs_theorem wikiPageWikiLink László_Lovász.
- Steinitzs_theorem wikiPageWikiLink Midsphere.
- Steinitzs_theorem wikiPageWikiLink Möbius_transformation.
- Steinitzs_theorem wikiPageWikiLink N-skeleton.
- Steinitzs_theorem wikiPageWikiLink Parallel_projection.
- Steinitzs_theorem wikiPageWikiLink Paul_Koebe.
- Steinitzs_theorem wikiPageWikiLink Planar_graph.
- Steinitzs_theorem wikiPageWikiLink Polyhedral_combinatorics.
- Steinitzs_theorem wikiPageWikiLink Polyhedral_graph.
- Steinitzs_theorem wikiPageWikiLink Polyhedron.
- Steinitzs_theorem wikiPageWikiLink Prism_graph.
- Steinitzs_theorem wikiPageWikiLink Projective_transformation.
- Steinitzs_theorem wikiPageWikiLink Riemann_series_theorem.
- Steinitzs_theorem wikiPageWikiLink Schlegel_diagram.
- Steinitzs_theorem wikiPageWikiLink Series-parallel_graph.
- Steinitzs_theorem wikiPageWikiLink Silhouette.
- Steinitzs_theorem wikiPageWikiLink Simple_graph.
- Steinitzs_theorem wikiPageWikiLink Skeleton_(topology).
- Steinitzs_theorem wikiPageWikiLink Stacked_polytope.
- Steinitzs_theorem wikiPageWikiLink Steinitz_exchange_lemma.
- Steinitzs_theorem wikiPageWikiLink Straight_skeleton.
- Steinitzs_theorem wikiPageWikiLink Tangent_circles.
- Steinitzs_theorem wikiPageWikiLink Tree_(graph_theory).
- Steinitzs_theorem wikiPageWikiLink Tutte_embedding.
- Steinitzs_theorem wikiPageWikiLink Two-dimensional_space.
- Steinitzs_theorem wikiPageWikiLink Undirected_graph.
- Steinitzs_theorem wikiPageWikiLink Unit_sphere.
- Steinitzs_theorem wikiPageWikiLink Upper_and_lower_bounds.
- Steinitzs_theorem wikiPageWikiLink Upper_bound.
- Steinitzs_theorem wikiPageWikiLink Vector_space.
- Steinitzs_theorem wikiPageWikiLink Vertex_(geometry).
- Steinitzs_theorem wikiPageWikiLink Vertex_(graph_theory).
- Steinitzs_theorem wikiPageWikiLink Vertex_connectivity.
- Steinitzs_theorem wikiPageWikiLink W._T._Tutte.
- Steinitzs_theorem wikiPageWikiLink Wheel_graph.
- Steinitzs_theorem wikiPageWikiLink William_Thurston.
- Steinitzs_theorem wikiPageWikiLink Y-Δ_transform.
- Steinitzs_theorem wikiPageWikiLink File:Equilibrium_stress.svg.
- Steinitzs_theorem wikiPageWikiLink File:Midsphere.png.
- Steinitzs_theorem wikiPageWikiLink File:Polyhedral_Delta-Y.svg.
- Steinitzs_theorem wikiPageWikiLink File:Schegel_diagram_as_shadow.png.
- Steinitzs_theorem wikiPageWikiLink File:Szilassi_polyhedron.svg.
- Steinitzs_theorem wikiPageWikiLinkText "Steinitz problem".
- Steinitzs_theorem wikiPageWikiLinkText "Steinitz realization".
- Steinitzs_theorem wikiPageWikiLinkText "Steinitz's theorem".
- Steinitzs_theorem wikiPageWikiLinkText "characterization of 1-skeleta".
- Steinitzs_theorem hasPhotoCollection Steinitzs_theorem.
- Steinitzs_theorem wikiPageUsesTemplate Template:Reflist.
- Steinitzs_theorem subject Category:Geometric_graph_theory.
- Steinitzs_theorem subject Category:Planar_graphs.