Flexible suspensions with a hexagonal equator

TL;DR

This paper constructs a flexible suspension with a hexagonal equator in 3D space and investigates its implications for the Strong Bellows Conjecture, which concerns scissors congruence of flexed polyhedra.

Contribution

It introduces a specific flexible suspension with a hexagonal equator and analyzes its properties in relation to the Strong Bellows Conjecture.

Findings

Constructed a non-immersed flexible suspension with a hexagonal equator.

Studied properties related to scissors congruence during flexing.

Provided insights into the Strong Bellows Conjecture for such structures.

Abstract

We construct a flexible (non immersed) suspension with a hexagonal equator in Euclidean 3-space and study its properties related to the Strong Bellows Conjecture which reads as follows: if an immersed polyhedron $\Cal P$ in Euclidean 3-space is obtained from another immersed polyhedron $\Cal Q$ by a continuous flex then $\Cal P$ and $\Cal Q$ are scissors congruent.