Rigid foldability, origami tessellation


Rigid foldability is an important characteristic of origami structures that becomes significant with non-paper materials. A rigidly foldable origami tessellation is one where the sectors remain rigid and all deflection occurs at the crease lines. Many rigidly foldable patterns have only one degree of freedom, making them potentially useful for deployable structures. Methods have been developed to construct rigidly foldable origami tessellations using materials with finite thickness based on zero-thickness rigidly foldable patterns. [Tachi 11].

Origami methods have been considered for application in deployable structures such as solar panels [Miura 85] [Zirbel et al. 13] and sterile shrouds [Francis et al. 13]. Other recent developments have included self-deployable origami stent grafts [Kuribayashi et al. 06], self-folding membranes [Pickett 07], and sandwich panel cores [Lebee and Sab 10]. A better understanding of how to create rigidly foldable tessellations can lead to previously unexplored applications.

This paper develops a method for evaluating the rigid foldability of origami tessellations by examining relationships between the dihedral angles in the pattern. The method is then used to determine what configurations allow origami twists, in particular, to be rigidly foldable. Rigidly foldable twists may be arrayed in a tessellation, providing a foundation for deployable origami-based structures to be constructed out of rigid materials.

Original Publication Citation

Thomas A. Evans, Robert J. Lang, Spencer P. Magleby, Larry L. Howell. Rigidly foldable origami gadgets and tessellations. R. Soc. open sci. 2015 2 150067; DOI: 10.1098/rsos.150067. Published 16 September 2015,

Document Type

Book Chapter

Publication Date


Permanent URL


American Mathematical Society




Ira A. Fulton College of Engineering and Technology


Mechanical Engineering