3 papers
math.CO2026
Deformations and second-order rigidity of polytopes
Matthias Adrian-Himmelmann, Martin Winter, Zhen Zhang
We study deformations of polytopes that preserve edge lengths and face coplanarities. This gives rise to a notion of rigidity, for which we develop a second-order theory together w…
math.MG2025
Spiderwebs on the Sphere and an Isoperimetric Theorem
Robert Connelly, Zhen Zhang
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 addition…
math.MG2024
Globally Rigid Convex Braced Polygons
Robert Connelly, Bill Jackson, Shin-ichi Tanigawa +1
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…