Flexible Polyhedra and Their Volumes

TL;DR

This paper reviews recent advances in the study of flexible polyhedra, focusing on the bellows conjecture that their volume remains constant during flexion, and discusses key methods and open problems.

Contribution

It provides a survey of recent results, methods, and open problems related to the volume invariance of flexible polyhedra and the bellows conjecture.

Findings

Confirmation of volume invariance during flexion for certain classes of polyhedra

Summary of main methods used to study flexible polyhedra

Identification of open problems in the field

Abstract

We discuss some recent results on flexible polyhedra and the bellows conjecture, which claims that the volume of any flexible polyhedron is constant during the flexion. Also, we survey main methods and several open problems in this area.