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Steinitz's theorem

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…

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Definitions and statement of the theorem

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Steinitz's theorem

Nodes113
Edges112
Triples71
Avg. degree1.98
Density0.017699
Components1

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Steinitz's theorem

Top relations

related to history · 22
Steinitz's theorem → Although, Branko Grünbaum, Convex Polytopes, Eades, Epifanov, Ernst Steinitz, Garvan, Grünbaum, Grünbaum's, James Clerk Maxwell, Luigi Cremona, Pierre Varignon, Richter-Gebert, Steinitz, Steinitz's, The, The Maxwell-Cremona, Theodore Motzkin, Truemper, Tutte
related to Specifying the shape of a face · 13
Steinitz's theorem → Another, Barnette, Grünbaum, However, In, Instead, It, Steinitz's, Such, This, Thus, Tutte, Tutte's
related to Proofs · 10
Steinitz's theorem → As, Balinski's, Cremona, Maxwell, One, Schlegel, Steinitz's, The, There, Tutte
related to Integer coordinates · 9
Steinitz's theorem → Apollonian, For, Geometrically, However, It, Some, Steinitz's, Subsequent, Writing
related to Tangent spheres · 9
Steinitz's theorem → Although, By, Circle, Dually, In, More, Möbius, Steinitz's, The
related to Definitions and statement of the theorem · 7
Steinitz's theorem → An, As, By Fáry's, Euclidean, From, Steinitz's, This
is a · 1
Steinitz's theorem → characterization of the undirected graphs formed by the edges and vertices of three-dimensional convex polyhedra

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Important terminology

graph theorem polyhedron polyhedral convex vertices planar edges face steinitz's every graphs given polyhedra vertex one faces displaystyle two realization

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Steinitz's theoremis acharacterization of the undirected graphs formed by the edges and vertices of three-dimensional convex polyhedra0.90text
Steinitz's theoremrelated to Definitions and statement of the theoremAn0.60section
Steinitz's theoremrelated to Definitions and statement of the theoremAs0.60section
Steinitz's theoremrelated to Definitions and statement of the theoremSteinitz's0.60section
Steinitz's theoremrelated to Definitions and statement of the theoremFrom0.60section
Steinitz's theoremrelated to Definitions and statement of the theoremThis0.60section
Steinitz's theoremrelated to Definitions and statement of the theoremEuclidean0.60section
Steinitz's theoremrelated to Definitions and statement of the theoremBy Fáry's0.60section
Steinitz's theoremrelated to historyThe0.60section
Steinitz's theoremrelated to historySteinitz's0.60section
Steinitz's theoremrelated to historyGrünbaum0.60section
Steinitz's theoremrelated to historyErnst Steinitz0.60section

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