发表机构
Georgia Institute of Technology; Harvard University（佐治亚理工学院; 哈佛大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
通过群论对折纸片材的线性周期模式进行分类，提出包含对称与拓扑约束的充分条件，并转化为设计原则，实现快速设计具有预定性能的新型折纸结构。
AI 中文摘要
广泛研究的折纸折痕图案（如Miura-ori）能够进行刚性折叠并保持其空间周期性。然而，周期性折痕图案通常需要额外的折痕，并折叠成准圆柱形状。在此，我们利用群论表明，此类片材的折叠性质很大程度上由其空间对称性（称为层群）决定。在每个对称类别中，允许的线性形状周期模式受到约束，并根据其所属的不可约表示进行分类。这种分类进一步给出了非线性应变模式存在的充分条件，该条件包含对称性约束和拓扑约束。通过这种方式，熟悉的特殊情况被置于一个统一框架内，该框架连接了对称性、网络拓扑和可展开性。最后，我们将分类结果转化为预测性设计原则，从而能够快速设计具有预定性能的新型片材。
英文摘要
Broadly studied origami crease patterns such as the Miura-ori are capable of rigid folding that maintains their spatial periodicity. However, periodic crease patterns generically require additional creases and fold into quasi-cylindrical shapes. Here, using group theory, we show that the folding properties of such sheets are largely determined by their spatial symmetries, known as layer groups. Within each symmetry class, the allowed linear shape-periodic modes of sheets are constrained and classified by the irreducible representation they belong to. Such classification further gives a sufficient condition, containing a symmetry constraint and a topological constraint, for the existence of a nonlinear strain mode. In this way, familiar special cases are placed within a unified framework that connects symmetry, network topology, and deployability. Finally, we turn our classification results into a predictive design principle that enables the rapid design of novel sheets with prescribed properties.
