On the development of the intersection of a plane with a polytope (Q1869734)
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scientific article; zbMATH DE number 1902825
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the development of the intersection of a plane with a polytope |
scientific article; zbMATH DE number 1902825 |
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On the development of the intersection of a plane with a polytope (English)
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28 April 2003
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The author investigates the polygonal intersections of the boundary of a convex 3-polytope and a 2-plane. Among other results, he proves that such a polygon yields a simple (i.e., non-selfintersecting) curve in a plane when this intersection is developed on that plane. (Here ``development'' is viewed as the result of unfolding flat a narrow strip surrounding that curve.) The main tool used by the author is a slight generalization of Cauchy's arm lemma. For an addendum, cf. [Commun. Korean Math. Soc. 22, No. 1, 121--122 (2007; Zbl 1168.53303)].
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polyhedron
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polytope
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unfolding
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boundary structure
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nets of convex polyhedra
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Cauchy's arm lemma
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