A new method for generalizing non-self-intersecting flexible polyhedra

TL;DR

This paper introduces a new construction method for generating a wide class of non-self-intersecting flexible polyhedral surfaces, expanding understanding of flexible structures with diverse topologies and applications.

Contribution

The paper presents the 'base + crinkle' method for creating flexible polyhedra that are non-triangulated, have multiple degrees of freedom, and various topologies, advancing geometric and engineering design.

Findings

Flexible polyhedra can be non-self-intersecting and non-triangulated.

The method enables polyhedra with multiple kinematic degrees of freedom.

Applications include origami, robotics, and metamorphic mechanisms.

Abstract

A surface is considered flexible if it allows a continuous deformation that preserves both metric and smoothness. We introduce a novel construction method, called 'base + crinkle,' for generating a broad class of non-self-intersecting flexible closed polyhedral surfaces (i.e. flexible polyhedra). These flexible polyhedra can be non-triangulated, exhibit multiple kinematic degrees of freedom, and possess topologies beyond the sphere. The geometric result provides fresh insights into the geometry of origami and the design of engineering mechanisms, such as sealed-chamber robotics and distortion-free metamorphic grippers.