Sabitov polynomials for volumes of polyhedra in four dimensions

Details Sabitov polynomials for volumes of polyhedra in four dimensions Sabitov polynomials for volumes of polyhedra in four dimensions

2011-08-30

arxiv.org/abs/1108.6014v2

Mathematics

Metric Geometry

23 pages; misprints corrected, Lemma 6.1 slightly rewritten, title changed

Scientific paper

In 1996 I.Kh. Sabitov proved that the volume of a simplicial polyhedron in a 3-dimensional Euclidean space is a root of certain polynomial with coefficients depending on the combinatorial type and on edge lengths of the polyhedron only. Moreover, the coefficients of this polynomial are polynomials in edge lengths of the polyhedron. This result implies that the volume of a simplicial polyhedron with fixed combinatorial type and edge lengths can take only finitely many values. In particular, this yields that the volume of a flexible polyhedron in a 3-dimensional Euclidean space is constant. Until now it has been unknown whether these results can be obtained in dimensions greater than 3. In this paper we prove that all these results hold for polyhedra in a 4-dimensional Euclidean space.

Affiliated with

Also associated with

No associations

Rating

Sabitov polynomials for volumes of polyhedra in four dimensions does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Sabitov polynomials for volumes of polyhedra in four dimensions, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Sabitov polynomials for volumes of polyhedra in four dimensions will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-729106