Zero-sum cycles in flexible non-triangular polyhedra

TL;DR

This paper extends the understanding of flexible polyhedra by establishing the existence of zero-sum cycles in non-triangular cases, building on prior work focused on triangular faces.

Contribution

It generalizes previous results by proving the existence of zero-sum cycles in flexible polyhedra with non-triangular faces, broadening the scope of geometric conditions for flexibility.

Findings

Existence of zero-sum cycles in non-triangular flexible polyhedra

Extension of previous results from triangular to non-triangular faces

Contribution to the geometric theory of flexible polyhedra

Abstract

Finding necessary conditions for the geometry of flexible polyhedra is a classical problem that has received attention also in recent times. For flexible polyhedra with triangular faces, we showed in a previous work the existence of cycles with a sign assignment for their edges, such that the signed sum of the edge lengths along the cycle is zero. In this work, we extend this result to flexible non-triangular polyhedra.