Here's a single-layer tensegrity I built based on a 4ν breakdown of the tetrahedron. I've long since taken it and the tensegrity octahedron you saw before apart. Those sharp wire ends made them a hazard to have around. I suppose I could have put a drop of white glue on the sharp part and that would have made it less painful to have around.
I called this a "Non-aligned Tensegrity Based on 4ν Tetrahedron". I completed assembling it on August 22, 1983. Structurally it was viable, but the dihedral angles about the strut didn't turn out as I had computed. I was wandering in the wilderness at this point. I still hadn't formulated my nonlinear programming approach to tensegrity design. That didn't start happening until April 4, 1985.