Globally Rigid Convex Braced Polygons

TL;DR

This paper introduces a new class of planar frameworks called braced polygons that can be globally rigid, drawing an analogy to convex polyhedra in 3D that are known to be rigid by classical theorems.

Contribution

It proposes and analyzes a novel class of planar frameworks, braced polygons, that exhibit global rigidity similar to convex polyhedra.

Findings

Braced polygons can be globally rigid in the plane.

The class extends concepts of rigidity from 3D convex polyhedra to 2D frameworks.

The work provides theoretical foundations for understanding rigidity in these structures.

Abstract

Here we propose a class of frameworks in the plane, braced polygons, that may be globally rigid and are analogous to convex polyopes in 3 space that are rigid by Cauchy's rigidity Theorem in 1813.