I received the elastic cord I wanted to use for The Affordable Tensegrity Toolkit, and prepared the first 30 stick prototype with it. The diameter of the cord fits nicely to the groove width, it wedges in and form a stable connection (within limits).
I build first a 30strut icosa with it, and was amazed about the bounce the final structure had. Instead of using a structure as template of the build, I had a generic weaving pattern in mind, following two simple rules. Once finished, I played with the icosa like a football, producing some domino effects with other structures.

30 strut icosahedron 
The next test consisted of timing the transformation from icosahedron into dodecahedron. That meant disassembling the icosa completely, and reusing the components in a different pattern. Again, I navigated through the build by its pattern, creating triangular corners around pentagonal faces. The structure warped itself in shape already while completing the third of twelve pentagons, and after eight minutes the transformation was complete.
I threw the dodecahedron quite lot around, which opened sometimes a corner. Playing it hard goes the limits of the attachment technique. This time I decided to time the disassembly by itself, less than two minutes to undo the sixty connections.

30 strut dodecahedron 
As expected, building the 6 strut tetrahedron proved most difficult, but cube and octahedron provided a fast, straight forward build. In a room without other sculptures, I started throwing the cube and octahedron quite hard against the wall. At some point, a tendon in the octahedron snapped, though I wasn't sure whether it was the impact or the way I held it before throwing.
After I replaced the tendon, I continued to bounce the models madly from wall to wall. This time I took care of holding the model mainly at the struts. I guess I limited the vigour I used for my experiments, although I used enough force to hear the tendons swishing during flight. Anyway, no more breakage occurred. The octahedron can safely be used for throwing games and bounced off walls. With all the fun I had finding out the stability limits by relatively brutal force, I look forward to more swishing, clicking and hitting sounds while doing some stress testing for the tensegrity toolkit.

30 struts in three different models 
You can reconfigure the model easily. Each single cord gets used as three tendons, two for the corner and one for the connection between corners. While building a model, aiming for similar length makes building easiest. Of course, as there are no markers each connection has to be guesstimated. When I played with different configuration of cube and octahedron, I noticed the dual quality. As two struts connect to each cord, you can place them very close together. The model can't collapse any more, yet seems more robust when thrown around.
Effectively, the total number of tendons reduces from 36 to 24. I'm not certain whether the proximity of the struts converts the 'missing' tendon into a kind of joint, however, by ignoring this tendon the remaining 24 tendons outline a cuboctahedron, the intersection between cube and octahedron. Both physical models look and behave similar in this configuration. By moving the struts together, they shaped four entwined triangles, like faces of a tetrahedron twisted inside and around. Reminds me of the jitterbug transformation, so I don't think I discovered something 'new', just new for me.

Four intertwined triangles in a 12strut pseudo cuboctahedron 
Intermezzo
I think the tetrahedron represent the number 2, the basic duality in universe. It contains as well the number 3. I see more threeness in the 6 faces of a cube and the 6 vertices of an octahedron, the 2by2ness appears in 4 edges constituting a face (cube) or converging into an edge (octahedron). Somehow, fiveness appears in the shapes observable. From a specific perspective, pentagonal outlines appear, all the while of hexagram and pentagram can be inscribed to some struts. Is there already the fiveness of the icosahedron in cube and octahedron?
In the 'orthogonal' cube, eliminating the 'middle' tendon doesn't create entwined triangles, yet brings two struts together along their length. The closer I moved the parallel struts together, the more familiar the structure appeared: it's a kind of 12strut icosahedron.

Orthogonal cube morphed into 12strut icosahedron 
The new cord material requires a bit more work to prepare the toolkit elements, but so far looks extremely promising to combine easy build methods with lasting tendons.