Embedded flexible spherical cross-polytopes with nonconstant volumes
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Publication:492204
DOI10.1134/S0081543815010058zbMath1322.52017arXiv1501.06198OpenAlexW2061293793MaRDI QIDQ492204
Publication date: 20 August 2015
Published in: Proceedings of the Steklov Institute of Mathematics (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1501.06198
Related Items (8)
Flexible polyhedra and their volumes ⋮ The spectrum of the Laplacian in a domain bounded by a flexible polyhedron in \(\mathbb{R}^d\) does not always remain unaltered during the flex ⋮ Recognition of affine-equivalent polyhedra by their natural developments ⋮ The Moscow Mathematical Society and metric geometry: from Peterson to contemporary research ⋮ Dehn invariant and scissors congruence of flexible polyhedra ⋮ A sufficient condition for a polyhedron to be rigid ⋮ On the Existence of Paradoxical Motions of Generically Rigid Graphs on the Sphere ⋮ Volumes of polyhedra in non-Euclidean spaces of constant curvature
Cites Work
- Generalization of Sabitov's theorem to polyhedra of arbitrary dimensions
- A counterexample to the rigidity conjecture for polyhedra
- The volume as a metric invariant of polyhedra
- The Bellows conjecture
- An example of a flexible polyhedron with nonconstant volume in the spherical space
- Sabitov polynomials for volumes of polyhedra in four dimensions
- Flexible cross-polytopes in spaces of constant curvature
- Algebraic methods for solution of polyhedra
- Lipschitzian Mappings and Total Mean Curvature of Polyhedral Surfaces. I
- Analytic structure of Schläfli function
- A generalized Heron-Tartaglia formula and some of its consequences
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