Sabitov polynomials for volumes of polyhedra in four dimensions

DOI10.1016/j.aim.2013.11.005zbMath1301.51027arXiv1108.6014OpenAlexW1974106266MaRDI QIDQ2445306

Alexander A. Gaifullin

Publication date: 14 April 2014

Published in: Advances in Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1108.6014

zbMATH Keywords

volumesimplicial complexresultantflexible polyhedronCayley-Menger determinantplace

Mathematics Subject Classification ID

(n)-dimensional polytopes (52B11) Length, area and volume in real or complex geometry (51M25) Solving polynomial systems; resultants (13P15)

Related Items (13)

Flexible polyhedra and their volumes ⋮ 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 ⋮ Generalization of Sabitov's theorem to polyhedra of arbitrary dimensions ⋮ Embedded flexible spherical cross-polytopes with nonconstant volumes ⋮ Deformations of period lattices of flexible polyhedral surfaces ⋮ Dehn invariant and scissors congruence of flexible polyhedra ⋮ Flexible cross-polytopes in spaces of constant curvature ⋮ The set of nondegenerate flexible polyhedra of a prescribed combinatorial structure is not always algebraic ⋮ A sufficient condition for a polyhedron to be rigid ⋮ Volumes of polyhedra in non-Euclidean spaces of constant curvature

Cites Work

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• Algebra versus analysis in the theory of flexible polyhedra
• Konstruktionsmethoden und das kombinatorische Homöomorphieproblem für Triangulationen kompakter semilinearer Mannigfaltigkeiten. (Methods of constructions and the combinatorical homeomorphism problem for triangulations of compact semilinear manifolds)
• A counterexample to the rigidity conjecture for polyhedra
• The volume as a metric invariant of polyhedra
• The Bellows conjecture
• Algebraic methods for solution of polyhedra
• Lipschitzian Mappings and Total Mean Curvature of Polyhedral Surfaces. I
• A generalized Heron-Tartaglia formula and some of its consequences

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