Deployable polyhedrons can transform between Platonic and Archimedean polyhedrons to meet the demands of various engineering applications. However, the existing design solutions are often with multiple degrees of freedom and complicated mechanism links and joints, which greatly limited their potential in practice. Combining the fundamentals of solid geometry and mechanism kinematics, this paper proposes a family of kirigami Archimedean polyhedrons based on the N-fold-symmetric loops of spatial 7R linkage, which perform one-DOF radial transformation following tetrahedral, octahedral, or icosahedral symmetry. Moreover, in each symmetric polyhedral group, three different transforming paths can be achieved from one identical deployed configuration. We also demonstrated that such design strategy can be readily applied to polyhedral tessellation. This work provides a family of rich solutions for deployable polyhedrons to facilitate their applications in aerospace exploration, architecture, metamaterials and so on.

翻译：可展开多面体能够实现柏拉图多面体与阿基米德多面体之间的转换，以满足各类工程应用需求。然而，现有设计方案通常具有多自由度及复杂的机构连杆与关节，严重限制了其实际应用潜力。本文结合立体几何基础与机构运动学原理，提出基于空间7R机构N重对称环路的一类剪纸型阿基米德多面体，该结构遵循四面体、八面体或二十面体对称性，可实现单自由度径向变换。此外，在每个对称多面体群中，可从同一展开构型实现三种不同的变换路径。我们进一步证明该设计策略可便捷应用于多面体镶嵌。本研究为可展开多面体提供了一类丰富的解决方案，以促进其在航空航天探测、建筑结构、超材料等领域的应用。