The Dehn invariants of the Bricard octahedra

TL;DR

This paper proves that the Dehn invariants of Bricard octahedra are invariant during flexing and confirms the Strong Bellows Conjecture for the Steffen flexible polyhedron, advancing understanding of flexible polyhedra.

Contribution

It establishes the invariance of Dehn invariants for Bricard octahedra and verifies the Strong Bellows Conjecture for the Steffen polyhedron, providing new insights into flexible polyhedral structures.

Findings

Dehn invariants of Bricard octahedra are constant during flexing

The Strong Bellows Conjecture holds for the Steffen flexible polyhedron

Advances understanding of invariants in flexible polyhedra

Abstract

We prove that the Dehn invariants of any Bricard octahedron remain constant during the flex and that the Strong Bellows Conjecture holds true for the Steffen flexible polyhedron.