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.
Publié le : 2005-08-15
Classification:
52B10,
51M20,
51M25,
52C25
@article{1127831442,
author = {Fedorchuk, Maksym and Pak, Igor},
title = {Rigidity and polynomial invariants of convex polytopes},
journal = {Duke Math. J.},
volume = {126},
number = {1},
year = {2005},
pages = { 371-404},
language = {en},
url = {http://dml.mathdoc.fr/item/1127831442}
}
Fedorchuk, Maksym; Pak, Igor. Rigidity and polynomial invariants of convex polytopes. Duke Math. J., Tome 126 (2005) no. 1, pp. 371-404. http://gdmltest.u-ga.fr/item/1127831442/