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.

中文翻译：

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4 折纸折纸顶点和镶嵌图案的山谷折痕重构

可重构折纸启发的折叠最近受到了极大的关注，因为它有可能通过折痕拓扑变形实现多种形状变化，从而使单一原始结构具有多功能性。然而，确定所有可能的山谷折痕 (MV) 分配是主要挑战之一，以确保刚性可折叠性并在大型 2D 折纸镶嵌或 3D 蜂窝结构中获得重复配置。在这项研究中，我们开发了一种简单的算法，结合图形表示和运动兼容性条件来评估具有 4 折痕顶点的折纸结构的可重构性，包括双波纹、Miura-ori 和对称 Eggbox 顶点，以及它们的 2D 甚至 3D细胞镶嵌。我们的分析揭示了三种类型的寡模态折纸镶嵌，其特征是独立于镶嵌尺寸的一致数量的 MV 分配，以及表现出负泊松比、零泊松比和正泊松比的多模态细胞折纸结构，并通过实验验证。这项工作可以作为开发基于通过山谷折痕分配的可重构折纸的多功能超材料和设备的垫脚石。