With more tautness than before, each strut could move laterally a lot more, and the network of tendons now distinctly outlines a tetrahedron. I wonder if an octahedron build like this could still collapse....
|Marsupial (Large tetrahedron mounted on 3-strut tensul with small tetrahedron suspended)|
|United Duals (Octahedron with a cube intersecting the edges)|
|Merkaba (stellated octahedron or octangula)|