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

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 flexible nondegenerate polyhedra combinatorially equivalent to $P$ is not algebraic.

8 pages, 4 figures

References in corpus (1)

• Sabitov polynomials for volumes of polyhedra in four dimensions