Rigidity of Circle Polyhedra in the 2-Sphere and of Hyperideal Polyhedra in Hyperbolic 3-Space

John C. Bowers, Philip L. Bowers, Kevin Pratt

We generalize Cauchy's celebrated theorem on the global rigidity of convex polyhedra in Euclidean $3$-space ${\mathbb{E}}^3$ to the context of circle polyhedra in the $2$-sphere $\…