5-connected 3-polytopes are refinements of octahedra (Q1068856)
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scientific article; zbMATH DE number 3931066
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | 5-connected 3-polytopes are refinements of octahedra |
scientific article; zbMATH DE number 3931066 |
Statements
5-connected 3-polytopes are refinements of octahedra (English)
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1987
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It is a consequence of a theorem of Steinitz that the boundary of every convex 3-dimensional polytope is a refinement of the boundary of a tetrahedron. By using discharging techniques, similar to the discharging techniques of Appel and Haken in their proof of the four-color problem, we show that the boundary of every 3-polytope with a 5-connected graph is a refinement of the boundary of an octahedron.
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discharging techniques
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3-polytope
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5-connected graph
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octahedron
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