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Sibirskii Matematicheskii Zhurnal, 2023, Volume 64, Number 2, Pages 252–275
DOI: https://doi.org/10.33048/smzh.2023.64.202
(Mi smj7759)
 

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
Full-text PDF (430 kB) Citations (2)
References:
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.
Funding agency Grant number
Ministry of Science and Higher Education of the Russian Federation FWNF-2022-0006
The work was carried out in the framework of the State Task to the Sobolev Institute of Mathematics (Project FWNF–2022–0006).
Received: 24.06.2021
Revised: 05.12.2022
Accepted: 10.01.2023
English version:
Siberian Mathematical Journal, 2023, Volume 64, Issue 2, Pages 269–286
DOI: https://doi.org/10.1134/S0037446623020027
Bibliographic databases:
Document Type: Article
UDC: 514.12
MSC: 52C25, 52B10, 51M25
Language: Russian
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
Citation in format AMSBIB
\Bibitem{Ale23}
\by V.~A.~Alexandrov
\paper Recognition of affine-equivalent polyhedra by their natural developments
\jour Sibirsk. Mat. Zh.
\yr 2023
\vol 64
\issue 2
\pages 252--275
\mathnet{http://mi.mathnet.ru/smj7759}
\crossref{https://doi.org/10.33048/smzh.2023.64.202}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3498588}
\transl
\jour Siberian Math. J.
\yr 2023
\vol 64
\issue 2
\pages 269--286
\crossref{https://doi.org/10.1134/S0037446623020027}
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