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Sibirskii Matematicheskii Zhurnal, 2024, Volume 65, Number 6, Pages 1076–1101
DOI: https://doi.org/10.33048/smzh.2024.65.603 (Mi smj7911) 		 
An embedded flexible polyhedron with nonconstant dihedral angles

V. A. Alexandrovab, E. P. Volokitinab

a Sobolev Institute of Mathematics, Novosibirsk, Russia
b Novosibirsk State University, Novosibirsk, Russia
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DOI: https://doi.org/10.33048/smzh.2024.65.603
Abstract: We construct some sphere-homeomorphic flexible self-intersection-free polyhedron in Euclidean 3-space whose all dihedral angles change during some flex. The polyhedron has 26 vertices, 72 edges, and 48 faces. To study the properties of the polyhedron, we use traditional geometric constructions and reasoning as well as symbolic calculations in the Wolfram Mathematica software system.
Keywords: Euclidean 3-space, flexible polyhedron, dihedral angle, short diagonal, segment-triangle intersection algorithm.
Funding agency Grant number
Ministry of Science and Higher Education of the Russian Federation FWNF-2022-0006
FWNF-2022-0005
The research was carried out within the State Task to the Sobolev Institute of Mathematics (Alexandrov was supported under Project FWNF–2022–0006 and Volokitin was supported under Project FWNF–2022–0005).
Received: 19.06.2024
Revised: 16.09.2024
Accepted: 23.10.2024
English version:
Siberian Mathematical Journal, 2024, Volume 65, Issue 6, Pages 1259–1280
DOI: https://doi.org/10.1134/S003744662406003X
Document Type: Article
UDC: 514.1
MSC: 52C25, 65D18, 68U05
Language: Russian
Citation: V. A. Alexandrov, E. P. Volokitin, “An embedded flexible polyhedron with nonconstant dihedral angles”, Sibirsk. Mat. Zh., 65:6 (2024), 1076–1101; Siberian Math. J., 65:6 (2024), 1259–1280
Citation in format AMSBIB
\Bibitem{AleVol24}
\by V.~A.~Alexandrov, E.~P.~Volokitin
\paper An~embedded flexible polyhedron with nonconstant dihedral angles
\jour Sibirsk. Mat. Zh.
\yr 2024
\vol 65
\issue 6
\pages 1076--1101
\mathnet{http://mi.mathnet.ru/smj7911}
\transl
\jour Siberian Math. J.
\yr 2024
\vol 65
\issue 6
\pages 1259--1280
\crossref{https://doi.org/10.1134/S003744662406003X}
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