Rigid-Foldable Polyhedral Origami

This paper introduces a novel origami pattern that enables the construction of polyhedral shapes from a planar sheet. The proposed polyhedral origami exhibits rigid foldability, which means that it can be folded without deforming its facets. The folding motion to a polyhedral shape can possess a single degree of freedom under the symmetric condition. A range of shapes, including pyramidal and prismatic shapes, can be created, depending on the design variables; and they can be folded into compact shapes for storage. Considering geometry, we derive mathematical conditions for the pattern design and investigate the folding process through kinematic analysis. Additionally, we conduct a parametric study of the effective volume and radius of its operational state. The proposed origami design will serve as a basic framework for developing foldable three-dimensional structures. It can have potential applications such as foldable space shields or deployable shelters made of thick materials for protection against space radiation.