The construction of 4-regular polyhedra containing triangles, quadrilaterals and pentagons (Q2853193)
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scientific article; zbMATH DE number 6217149
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | The construction of 4-regular polyhedra containing triangles, quadrilaterals and pentagons |
scientific article; zbMATH DE number 6217149 |
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18 October 2013
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convex polyhedron
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4-regular polyhedron
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0.8675983
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0.8664494
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0.86380744
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The construction of 4-regular polyhedra containing triangles, quadrilaterals and pentagons (English)
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Let \(P\) denote a 3-dimensional (convex) polytope or a polyhedral graph. A polyhedron \(P\) is \(k\)-regular if all its vertices have the same degree \(k\). Using belts and hats as building patches, two new classes of 4-regular polyhedra containing pentagons are constructed. One has only faces of 3-gons and 5-gons, the other has faces of 3-gons, 4-gons and 5-gons. Furthermore, the sufficient and necessary condition for their existence is given.
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