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The set of nondegenerate flexible polyhedra of a prescribed combinatorial structure is not always algebraic

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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.

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Authors and Affiliations

  1. Sobolev Institute of Mathematics, Novosibirsk, Russia

    V. A. Alexandrov

  2. Russia Novosibirsk State University, Novosibirsk, Russia

    V. A. Alexandrov

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  1. V. A. Alexandrov
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Correspondence to V. A. Alexandrov.

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Original Russian Text Copyright © 2015 Alexandrov V.A.

Novosibirsk. Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 56, No. 4, pp. 723–731, July–August, 2015; DOI: 10.17377/smzh.2015.56.401.

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Alexandrov, V.A. The set of nondegenerate flexible polyhedra of a prescribed combinatorial structure is not always algebraic. Sib Math J 56, 569–574 (2015). https://doi.org/10.1134/S0037446615040011

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  • DOI: https://doi.org/10.1134/S0037446615040011

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