Self-equilibrium and super-stability of rhombic truncated regular tetrahedral and cubic tensegrities using symmetry-adapted force-density matrix method

•Form-finding of rhombic truncated regular tetrahedral and cubic tensegrities are studied.•Their force-density matrices are block-diagonalized using group representation theory.•Conditions for their self-equilibrium and super-stability are analytically established.•These tensegrities help to develop biomechanical models, metamaterials, and robotics.