  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.
