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Sibirskii Matematicheskii Zhurnal, 2015, Volume 56, Number 4, Pages 723–731
DOI: https://doi.org/10.17377/smzh.2015.56.401 (Mi smj2673) 		 
The set of nondegenerate flexible polyhedra of a prescribed combinatorial structure is not always algebraic

V. A. Alexandrovab

a Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk, Russia
b Novosibirsk State University, Physics Department, Novosibirsk, Russia
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DOI: https://doi.org/10.17377/smzh.2015.56.401
Abstract: We construct some example of a closed nondegenerate nonflexible polyhedron $P$ in Euclidean $3$-space that is the limit of a sequence of nondegenerate flexible polyhedra each of which is combinatorially equivalent to $P$. This implies that the set of nondegenerate flexible polyhedra combinatorially equivalent to $P$ is not algebraic.
Keywords: flexible polyhedron, dihedral angle, Bricard octahedron, algebraic set.
Received: 25.11.2013
Revised: 15.06.2015
English version:
Siberian Mathematical Journal, 2015, Volume 56, Issue 4, Pages 569–574
DOI: https://doi.org/10.1134/S0037446615040011
Bibliographic databases:
Document Type: Article
UDC: 514.113.5
Language: Russian
Citation: V. A. Alexandrov, “The set of nondegenerate flexible polyhedra of a prescribed combinatorial structure is not always algebraic”, Sibirsk. Mat. Zh., 56:4 (2015), 723–731; Siberian Math. J., 56:4 (2015), 569–574
Citation in format AMSBIB
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