Here are the three early six-strutted tensegrities I assembled. From left to right they are the tensegrity icosahedron, the tensegrity tetrahedron and the tensegrity vector equilibrium. The tensegrity icosahedron was fabricated in 1949 by Buckminster Fuller after seeing Kenneth Snelson's Early X Piece. You can read more about it in Section 2.3 of my book. The previous photo will tell you all about the tensegrity vector equilibrium.
The tensegrity tetrahedron is discussed in Section 2.4 of my book. It was first exhibited by Francesco della Sala at the University of Michigan in 1952. This particular one has equal-length tendons. It took the most work of any of them to design. A lot of that work was formulating a model and deriving equations which took me from July 12 to 23, 1981. To get equal-length tendons, I maximized the struts lengths subject to the tendon lengths all being equal. I wrote a FORTRAN program to do it with the assistance of the ZXGSP routine in the IMSL numerical package which Tufts Computing Center had at the time. I got strut lengths of 3.898 when the second power of the tendon lengths was three.