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15 August 2005 Rigidity and polynomial invariants of convex polytopes
Maksym Fedorchuk, Igor Pak
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Duke Math. J. 129(2): 371-404 (15 August 2005). DOI: 10.1215/S0012-7094-05-12926-X

Abstract

We present an algebraic approach to the classical problem of constructing a simplicial convex polytope given its planar triangulation and lengths of its edges. We introduce polynomial invariants of a polytope and show that they satisfy polynomial relations in terms of squares of edge lengths. We obtain sharp upper and lower bounds on the degree of these polynomial relations. In a special case of regular bipyramid we obtain explicit formulae for some of these relations. We conclude with a proof of the Robbins conjecture on the degree of generalized Heron polynomials.

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Maksym Fedorchuk. Igor Pak. "Rigidity and polynomial invariants of convex polytopes." Duke Math. J. 129 (2) 371 - 404, 15 August 2005. https://doi.org/10.1215/S0012-7094-05-12926-X

Information

Published: 15 August 2005
First available in Project Euclid: 27 September 2005

zbMATH: 1081.52012
MathSciNet: MR2165546
Digital Object Identifier: 10.1215/S0012-7094-05-12926-X

Subjects:
Primary: 52B10
Secondary: 51M20 , 51M25 , 52C25

Rights: Copyright © 2005 Duke University Press

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Vol.129 • No. 2 • 15 August 2005
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