Mountain-valley crease reconfiguration of 4-crease origami vertices and tessellations

Reconfigurable origami-inspired folding has recently gained significant attention due to its potential to achieve multi-shape changes through crease topological morphing, resulting in multi-functionality from a single original structure. However, it is one of the major challenges to determine all possible mountain-valley crease (MV) assignments that ensure rigid foldability and obtain duplicate configurations in large 2D origami tessellations or 3D cellular structures. In this study, we developed a straightforward algorithm that combines graphic representation and motion compatibility conditions to assess the reconfigurability of origami structures with 4-crease vertices including double corrugated, Miura-ori, and symmetric Eggbox vertices, as well as their 2D and even 3D cellular tessellations. Our analysis has revealed three types of oligo-modal origami tessellations characterised by a consistent number of MV assignments independent of tessellation size, and pluri-modal cellular origami structures that exhibit negative, zero, and positive Poisson's ratios which were verified through experiment. This work could serve as a stepping stone towards developing multifunctional metamaterials and devices based on reconfigurable origami through mountain-valley crease assignment.