A flexible polyhedron without self-intersections in Euclidean 3-space, all of whose dihedral angles change during a flex

TL;DR

This paper presents a construction of a flexible polyhedron in Euclidean 3-space that remains free of self-intersections while all its dihedral angles change during flexion, demonstrating new flexibility properties.

Contribution

We introduce a novel flexible polyhedron with all dihedral angles varying during flexion, expanding understanding of polyhedral flexibility without self-intersections.

Findings

Polyhedron has 26 vertices, 72 edges, 48 faces.

All dihedral angles change during flex.

Polyhedron remains self-intersection free during flex.

Abstract

We construct a sphere-homeomorphic flexible self-intersection free polyhedron in Euclidean 3-space such that all its dihedral angles change during some flex of this polyhedron. The constructed polyhedron has 26 vertices, 72 edges and 48 faces. To study its properties, we use symbolic computations in the Wolfram Mathematica software system.