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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.
MSC:
52C25 Rigidity and flexibility of structures (aspects of discrete geometry)
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