Besides icosahedra, octahedra can be build to collapse and bounce back. If you use just elastic cords, the model has high mobility, yet I noticed that the cords slide sometimes to easy around in models with just elastic cord. I use elastics for the six 'corner' loops, and nylon for the remaining twelve tendons.
The less stretchy nylon helps to maintain the overall shape after a collapse. The different materials indicate their function in a 'solid' octahedron: The edges turned into the nylon cords, the corners folded open into a square loop made of elastic cord.
The nylon cord has a length of 7cm between the knots (made from 10cm cuts), the elastic cord has a length of 30cm tied to a loop. As I loop the the elastic cord around the grooves to secure their position, the effective length between struts comes down to 6cm. The struts itself measure 16cm, with 15 cm between attachment points.
Components for the model
I aim for precision when I prepare the components for a model, yet symmetrical models can do with a bit of variation in length. With a lot of a variation in tendon or strut length, the model looks less symmetrical, it still works as tensegrity system.
So it starts from 12 struts (15cm effective compression), 6 loops made from elastic cord, 12 tendons made from nylon. The four 'horizontal' edges will be yellow, the eight vertical ones will be orange. Different colours for different functional elements make it easier to keep organised while the model is still two-dimensional.
Step 1: Attaching the tendons
In the finished model, each strut is connected to two tendons and member of two 'corner loops'. To prevent the tendons from slipping out, they get attached first. Four struts get a 'vertical' and 'horizontal' edge attached, four struts get the remaining four verticals and four remain empty.
Step 2: The bottom corner
The struts with only vertical tendons end up in the bottom of the model. The struts are connected into a loop on the end with the tendon, so that the knots point to the 'inside' of the loop, the longer end goes away from the loop. (This means that if the struts fold over clockwise, the knot will be clockwise towards the strut as well). I start usually with the opposing corners, so that I can always half the tendon when connecting an additional strut. The elastic is looped around the groove once to secure it in place.
Step 3: The top corner
The top corner is assembled in the same way - connecting four struts at the end with the vertical (orange) tendons, knots points inside, tendons to the outside. All corner need to fold with the same chirality, ie clockwise or counterclockwise. If you lay the top corner above the bottom corner, the yellow tendons should already point to the strut of the bottom corner it connects to.
Step 4: Connecting top and bottom corners with horizontal tendons
Depending on the length of the struts, and the tightness of fit of the cords and grooves, a lot of slipping and sliding can happen while connecting top and bottom corners. Once we yellow tendons were in place, I took care that the loops didn't get entangled. At this stage, the struts hold each other up, like in the match head trick.
Step 5: Connecting top and bottom corner with remaining corners
This step unveils the precision of planning and preparing of this process. With a good loop length, the model will start to erect itself, becoming three-dimensional and easing the following steps. The inside-outsideness of the remaining corners is still more of an up-downness when the elastic are connected. The inside of the loops goes along the bottom half of the bottom corner strut, and the top half of the top corner strut. If the struts still fold over un-entangled, the top corner starts pushing up the more corners connect to it. Now it's a good time to check that the free ends of the vertical tendons hang in a decent direction.
Step 6: Connecting the remaining struts to the tendons
Over and under become more important now, and make life easier at the same time. The remaining struts connect between a bottom and top. Each strut goes under a top corner strut, attaches to the bottom corner tendons on the strut in the same direction as in the top corner. It attaches also the top corner tendon of the top corner strut that runs parallel to the one crossed under. (I wonder if this description makes any sort of sense unless you starting these three-dimensional puzzles yourself).
If all worked fine, the top end of the newly connected strut pull on the top corner and float a bit.
Step 7: Connecting the top part of the middle corners
A lot of movement will happen now. only eight connections finalise the model. Depending on how much uncontrolled movement happens, the model might fall apart or become lose. Working patiently with a steady hands prevents the frustration that arises from the anticipation of success and the sight of an entangled mess of sticks and strings. Like with the other loop connections, the knot of the tendon need to point in the same direction as the other struts in the loop.
Step 8: Connecting the bottom part of the middle corners
If the cords can slide easily, this step can become tricky. If the tendons and loops are too short, the model might 'fly apart', with too long cord lengths the model will still lay collapsed in a pile. Once the remaining connections are made, I take some time to 'tune' each corner. It's more likely to have some trapezoidal corners instead of nice squared ones. If struts were accidentally 'twisted' during build, they can be turned into the proper direction, so that each corner looks similar (all knots oriented the same way, elastic cords length equally from strut to strut.
Step 9: Test
Now the model can be loaded to collapse. With too long loops, a model might still look like this - well, a bit more chaotic as the elastic string would dangle around somewhere. That happened to me with the very first octahedron I build. I went from corner to corner and looped the elastic several times around each corner, and slowly the structure started 'working'. With sufficient pre-tension the model can be handled and tuned easily, and minor hick-ups during the build process corrected.
Sorry for mixing up the photos - two of the steps show a different octahedron. Anyway, if you happened to notice this error it's about time to start building tensegrities.