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Sibirsk. Mat. Zh., 2015, Volume 56, Number 4, Pages 723–731 (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

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.

DOI: https://doi.org/10.17377/smzh.2015.56.401

Full text: PDF file (269 kB)
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English version:
Siberian Mathematical Journal, 2015, 56:4, 569–574

Bibliographic databases:

Document Type: Article
UDC: 514.113.5
Received: 25.11.2013
Revised: 15.06.2015

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

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