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This article is cited in 2 scientific papers (total in 2 papers)
Recognition of affine-equivalent polyhedra by their natural developments
V. A. Alexandrovab a Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk
b Novosibirsk State University
Abstract:
The classical Cauchy rigidity theorem for convex polytopes reads that if two convex polytopes have isometric developments then they are congruent. In other words, we can decide whether two convex polyhedra are isometric or not by only using their developments. We study a similar problem of whether it is possible to understand that two convex polyhedra in Euclidean 3-space are affine-equivalent by only using their developments.
Keywords:
Euclidean 3-space, convex polyhedron, development of a polyhedron, Cauchy rigidity theorem, affine-equivalent polyhedra, Cayley–Menger determinant.
Received: 24.06.2021 Revised: 05.12.2022 Accepted: 10.01.2023
Citation:
V. A. Alexandrov, “Recognition of affine-equivalent polyhedra by their natural developments”, Sibirsk. Mat. Zh., 64:2 (2023), 252–275; Siberian Math. J., 64:2 (2023), 269–286
Linking options:
https://www.mathnet.ru/eng/smj7759 https://www.mathnet.ru/eng/smj/v64/i2/p252
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