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Continuous deformations of polyhedra that do not alter the dihedral angles. (English) Zbl 1301.52037
The author proves that in hyperbolic and spherical 3-spaces there are compact non-convex polyhedral surfaces homeomorphic to the sphere that can be non-trivially continuously deformed in such a way that all the dihedral angles are preserved. Here a non-trivial deformation means that it changes the surface area, the total mean curvature, and the Gaussian curvature of some vertex.
MSC:
52C25 Rigidity and flexibility of structures (aspects of discrete geometry)
52B70 Polyhedral manifolds
52C22 Tilings in \(n\) dimensions (aspects of discrete geometry)
51M20 Polyhedra and polytopes; regular figures, division of spaces
51K05 General theory of distance geometry
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