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 Sibirsk. Mat. Zh., 2012, Volume 53, Number 4, Pages 892–910 (Mi smj2371)

Description of the combinatorial structure of algorithmically $1$-parametric polyhedra of spherical type

I. G. Maksimov

Ministry for Education of the Moscow Region, Krasnogorsk, Russia

Abstract: We consider one of the problems of the theory of flexible polyhedra – the problem about the number of the parameters that must be defined additionally to the edge lengths for a polyhedron of a given combinatorial type in order to exclude its possible bendings. We give a description for the combinatorial structure of polyhedra of spherical type for which this number is equal to $1$.

Keywords: flexible polyhedron, bending, algorithm.

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English version:
Siberian Mathematical Journal, 2012, 53:4, 718–731

Bibliographic databases:

UDC: 514.113+514.772.35
Revised: 14.11.2011

Citation: I. G. Maksimov, “Description of the combinatorial structure of algorithmically $1$-parametric polyhedra of spherical type”, Sibirsk. Mat. Zh., 53:4 (2012), 892–910; Siberian Math. J., 53:4 (2012), 718–731

Citation in format AMSBIB
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\by I.~G.~Maksimov
\paper Description of the combinatorial structure of algorithmically $1$-parametric polyhedra of spherical type
\jour Sibirsk. Mat. Zh.
\yr 2012
\vol 53
\issue 4
\pages 892--910
\mathnet{http://mi.mathnet.ru/smj2371}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3013534}
\transl
\jour Siberian Math. J.
\yr 2012
\vol 53
\issue 4
\pages 718--731
\crossref{https://doi.org/10.1134/S0037446612040131}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84865454697}

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Citing articles on Google Scholar: Russian citations, English citations
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This publication is cited in the following articles:
1. V. A. Alexandrov, “The set of nondegenerate flexible polyhedra of a prescribed combinatorial structure is not always algebraic”, Siberian Math. J., 56:4 (2015), 569–574
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