Spiderwebs on the Sphere and an Isoperimetric Theorem

TL;DR

This paper establishes a rigidity theorem for certain inscribed polytopes on a sphere, using classical isoperimetric methods to analyze frameworks and their geometric constraints.

Contribution

It introduces a new rigidity result for spherical polytopes with specific conditions, combining geometric and topological approaches.

Findings

Proves a rigidity theorem for inscribed spherical polytopes

Uses classical isoperimetric ideas in the proof

Identifies conditions under which polytopes are rigid

Abstract

Here we present a rigidity result in a global (semi-global, homotopy) setting for a restrictive class of polytopes, those that can be inscribed in a unit sphere, with some additional conditions. The proof of the rigidity result for cabled frameworks on the surface of the sphere uses classical isoperimetric ideas.