Folded isometric deformations and banana-shaped seedpod

Thin vegetal shells have recently been a significant source of inspiration for the design of smart materials and soft actuators. Herein is presented a novel analytical family of isometric deformations with a family of θ-folds crossing a family of parallel z-folds; it contains the isometric deformations of a banana-shaped surface inspired by a seedpod, which converts a vertical closing into either an horizontal closing or an opening depending on the location of the fold. Similarly to the seedpod, optimum shapes for opening ease are the most elongated ones.