Kirigami Archimedean Polyhedrons with One‐Degree of Freedom Radial Transformation

Deployable polyhedrons can transform between Platonic and Archimedean polyhedrons to meet the demands of various engineering applications. However, the existing design solutions often with multiple degrees of freedom and complicated mechanism links and joints, which greatly limit 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 7 R linkages that enable one‐degree of freedom (one‐DOF) radial transformation following tetrahedral, octahedral, and icosahedral symmetry. In each symmetric polyhedral group, three different transforming paths are achieved from one identical deployed configuration to three different deployed configurations. Meanwhile, the one‐DOF transformations among all five Platonic polyhedrons and the corresponding Archimedean polyhedrons are revealed following regular geometry. Furthermore, the reconfigurable kirigami polyhedrons are constructed by superimposed patterns, whose various thermal responses based on the different layout cases of bi‐material strips are demonstrated via experiments. This work provides a family of rich solutions for deployable polyhedrons to facilitate their applications in aerospace exploration, architecture, metamaterials, and so on.