The Stress-Flex Conjecture

TL;DR

This paper introduces the stress-flex conjecture, proposing that certain coned polytope frameworks are prestress stable, supported by numerical experiments suggesting broader applicability beyond convex cases and higher genus polytopes.

Contribution

It formulates the new stress-flex conjecture and provides numerical evidence for its validity across various polytope types and topologies.

Findings

Numerical experiments support the stress-flex conjecture.

Coned polytope frameworks may be prestress stable.

Conjecture appears valid beyond convex and higher genus polytopes.

Abstract

Recently, it has been proven that a tensegrity framework that arises from coning the one-skeleton of a convex polytope is rigid. Since such frameworks are not always infinitesimally rigid, this leaves open the question as to whether they are at least prestress stable. We prove here that this holds subject to an intriguing new conjecture about coned polytope frameworks, that we call the stress-flex conjecture. Multiple numerical experiments suggest that this conjecture is true, and most surprisingly, seems to hold even beyond convexity and also for higher genus~polytopes.