Self-equilibrium and super-stability of truncated regular hexahedral and octahedral tensegrity structures

This paper presents conditions for self-equilibrium as well as super-stability of the truncated regular hexahedral and octahedral tensegrity structures. Their symmetry can be described by octahedral group in group representation theory, and furthermore, their force density matrix is analytically rewritten in the symmetry-adapted form. The condition for self-equilibrium, in terms of force densities, is found by satisfying the non-degeneracy condition for a tensegrity structure. The condition for super-stability, also in terms of force densities, is further presented by guaranteeing positive semi-definiteness of the force density matrix