The configuration space of equilateral and equiangular hexagons

TL;DR

This paper characterizes the configuration space of equilateral, equiangular hexagons, revealing isolated and deformable configurations with explicit shape descriptions.

Contribution

It provides explicit expressions for all shapes of such hexagons and analyzes their deformation spaces, including isolated and continuous configurations.

Findings

Chair configuration is isolated in the space.

Boat configuration admits one-dimensional deformations forming a circle.

Explicit shape expressions for all configurations.

Abstract

We study the configuration space of equilateral and equiangular spatial hexagons for any bond angle by giving explicit expressions of all the possible shapes. We show that the chair configuration is isolated, whereas the boat configuration allows one-dimensional deformations which form a circle in the configuration space.