A unified solution for self-equilibrium and super-stability of rhombic truncated regular polyhedral tensegrities

As a novel class of lightweight and reticulated structures, tensegrities have found a diversity of technologically significant applications. In this paper, we theoretically investigate the self-equilibrium and super-stability of rhombic truncated regular polyhedral (TRP) tensegrities. First, the analytical solutions are derived individually for rhombic truncated tetrahedral, cubic, octahedral, dodecahedral, and icosahedral tensegrities. Based on these solutions, we establish a unified analytical expression for rhombic TRP tensegrities. Then the necessary and sufficient condition that ensures the existence of a self-equilibrated and super-stable state is provided. The obtained solutions are helpful not only for the design of self-equilibrated and super-stable tensegrities but also for their applications in biomechanics, civil and aerospace engineering.