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The set of nondegenerate flexible polyhedra of a prescribed combinatorial structure is not always algebraic. (English. Russian original) Zbl 1327.52037
Sib. Math. J. 56, No. 4, 569-574 (2015); translation from Sib. Mat. Zh. 56, No. 4, 723-731 (2015).
Summary: 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.
52C25 Rigidity and flexibility of structures (aspects of discrete geometry)
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