Generalization of Sabitov's theorem to polyhedra of arbitrary dimensions
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Publication:464730
DOI10.1007/s00454-014-9609-2zbMath1314.52008arXiv1210.5408OpenAlexW2065249655MaRDI QIDQ464730
Publication date: 29 October 2014
Published in: Discrete \& Computational Geometry (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1210.5408
(n)-dimensional polytopes (52B11) Length, area, volume and convex sets (aspects of convex geometry) (52A38) Combinatorial aspects of simplicial complexes (05E45)
Related Items (13)
Flexible polyhedra and their volumes ⋮ How many times can the volume of a convex polyhedron be increased by isometric deformations? ⋮ Necessary conditions for the extendibility of a first-order flex of a polyhedron to its flex ⋮ 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 ⋮ Euclidean volumes of hyperbolic knots ⋮ The Moscow Mathematical Society and metric geometry: from Peterson to contemporary research ⋮ Embedded flexible spherical cross-polytopes with nonconstant volumes ⋮ Algebraic vertices of non-convex polyhedra ⋮ Deformations of period lattices of flexible polyhedral surfaces ⋮ Dehn invariant and scissors congruence of flexible polyhedra ⋮ Flexible cross-polytopes in spaces of constant curvature ⋮ A sufficient condition for a polyhedron to be rigid ⋮ Volumes of polyhedra in non-Euclidean spaces of constant curvature
Cites Work
- A counterexample to the rigidity conjecture for polyhedra
- The volume as a metric invariant of polyhedra
- The Bellows conjecture
- Sabitov polynomials for volumes of polyhedra in four dimensions
- Flexible cross-polytopes in spaces of constant curvature
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