Unfolding a twist hidden in origami structures

Over the past 50 years, origami — the art of paper folding — has evolved into a distinct scientific and engineering discipline. Owing to its broad potential applications, it has revolutionized the design of foldable, lightweight structures for aerospace engineering, robotics, biomedical devices, antennas, shock absorbers, and metamaterials.

An internal twist mechanism was originally discovered by Pooya Sareh in crystallographic tessellations based on the Miura origami pattern. Biruta Kresling explored this phenomenon, dubbing it the “Sareh twist.”

Kresling extended and generalized the description of this twisting phenomenon to origami structures that fold naturally under external loads, such as paper cones with a single collapsing point or paper tubes with multiple collapsing points. The latter configuration is known as the Kresling pattern.

In one model, she combined a Sareh twist before folding with its flat-folded “twin.” This “twin-twist” model demonstrated the geometrical relationship between two extreme states of folding, allowing further visualization of the twist.

She also introduced a framework that leverages geometric symmetries to fragment complex forms into constituent Sareh units.

“This work uncovers a previously hidden geometric principle underlying a twist mechanism that emerges from the simultaneous rotation of a movable sector about two wide-angled pivot axes belonging to the opposite sector within a single unit,” Kresling said. “Identifying this specific symmetry condition enables the determination of the parameters that ensure optimal functionality in tessellation crease patterns, thereby advancing the theoretical understanding and practical design of deployable structures.”

The findings suggest that considering the Sareh twist as an essential design element can optimize the efficiency and predictability of folding structures for various applications.

Source: “The Sareh twist: A hidden geometric principle in origami tessellations,” by Biruta Kresling, Journal of Applied Physics (2026). The article can be accessed at https://doi.org/10.1063/5.0304558 .