A rigidity criterion for non-convex polyhedra

Details A rigidity criterion for non-convex polyhedra A rigidity criterion for non-convex polyhedra

2003-01-28

arxiv.org/abs/math/0301333v2

Discrete and Computational Geometry, 33 (2005):2, 207-221.

Mathematics

Differential Geometry

11 pages, 1 image. Revised versions will be posted on http://picard.ups-tlse.fr/~schlenker v2: one statement corrected, ref. a

Scientific paper

Let $P$ be a (non necessarily convex) embedded polyhedron in $\R^3$, with its vertices on an ellipsoid. Suppose that the interior of $P$ can be decomposed into convex polytopes without adding any vertex. Then $P$ is infinitesimally rigid. More generally, let $P$ be a polyhedron bounding a domain which is the union of polytopes $C_1, ..., C_n$ with disjoint interiors, whose vertices are the vertices of $P$. Suppose that there exists an ellipsoid which contains no vertex of $P$ but intersects all the edges of the $C_i$. Then $P$ is infinitesimally rigid. The proof is based on some geometric properties of hyperideal hyperbolic polyhedra.

Affiliated with

Also associated with

No associations

Rating

A rigidity criterion for non-convex polyhedra 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 A rigidity criterion for non-convex polyhedra, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and A rigidity criterion for non-convex polyhedra will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-317350