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Recognition of affine-equivalent polyhedra by their natural developments Full article

Journal Siberian Mathematical Journal
ISSN: 0037-4466 , E-ISSN: 1573-9260
Output data Year: 2023, Volume: 64, Number: 2, Pages: 269-286 Pages count : 18 DOI: 10.1134/S0037446623020027
Tags Euclidean 3-space, convex polyhedron, development of a polyhedron, Cauchy rigidity theorem, affine-equivalent polyhedra, Cayley-Menger determinant
Authors Alexandrov V.A. 1,2
Affiliations
1 Sobolev Institute of Mathematics
2 Department of Physics, Novosibirsk State University

Funding (1)

1 Sobolev Institute of Mathematics FWNF-2022-0006

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.
Cite: Alexandrov V.A.
Recognition of affine-equivalent polyhedra by their natural developments
Siberian Mathematical Journal. 2023. V.64. N2. P.269-286. DOI: 10.1134/S0037446623020027 WOS Scopus РИНЦ OpenAlex
Original: Александров В.А.
Распознавание аффинно-эквивалентных многогранников по их натуральным разверткам
Сибирский математический журнал. 2023. Т.64. №2. С.252-275. DOI: 10.33048/smzh.2023.64.202 РИНЦ
Dates:
Submitted: Jun 24, 2021
Accepted: Jan 10, 2023
Published print: Mar 24, 2023
Published online: Mar 24, 2023
Identifiers:
Web of science: WOS:000984262300002
Scopus: 2-s2.0-85151091280
Elibrary: 61120374
OpenAlex: W3175127300
Citing:
DB Citing
Scopus 1
Web of science 1
OpenAlex 1
Elibrary 1
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