New Euler relation questions for convex 3-dimensional polytopes (Q2837314)
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scientific article; zbMATH DE number 6186466
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | New Euler relation questions for convex 3-dimensional polytopes |
scientific article; zbMATH DE number 6186466 |
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10 July 2013
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Euler's formula
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Eberhard's Theorem
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3-polytopal graph
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3-polytopes
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New Euler relation questions for convex 3-dimensional polytopes (English)
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The Eberhard's Theorem and its consequences have been widely investigated by several authors e.g. \textit{B. Grünbaum} gave in [Convex polytopes. 2nd ed. New York, NY: Springer (2003; Zbl 1024.52001)] a simple complete proof utilizing graphs and Steinitz's Theorem. He also considered a 4-valent analogue of Eberhard's Theorem using the Euler formula. The author in this paper shows some new possibilities and examples related to the above topic. His investigation is restricted to 3-polytopal graphs but generalizations to other plane connected graphs are possible.
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0.7847190499305725
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0.7747893333435059
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0.7559361457824707
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