How to build an octahedron with the Affordable Tensegrity toolkit

You can build an octahedron (eight triangular faces, twelve edges and six corners joining four edges each) out of twelve identical elements. The cord gives the strut an orientation, a back and front. The knotted end points in clockwise direction when viewed from the front.

Single toolkit element

This orientation determines the twist of the tension element, and helps following simple rules during the build phase. Here goes the first one:
Tendons go along the front of the strut, which means the 'outside' of the finished structure.

The first connection

First, an element connects to the tendon of another. The distance is about one third of the total tendon, for simplicity I call this the 'short end'. Both struts lie on their 'back', the knot in the connection points towards the short end, the knot in the short end points clockwise.

Continuing the pattern

The third strut repeats the same idea: The knot points towards the short end, the short end of the newly connected strut rests upon the strut it threaded in. The next rule becomes apparent:
The knots point towards the end of the strut, not the center.

Four struts form one 'corner'

With the fourth strut one corner of the octahedron is finished. All knots should now point towards the short end of the next strut in the square, and the struts intersect in clockwise direction like in the photo.

Two corners

Preparing top and bottom corner makes the final assembly easier. Simply connect four more struts exactly the way you did before. Put it aside until later

The next vital connection

From now on, things get more three-dimensional and require a bit confidence that everything holds together. Each of the tendons connects to two other struts in the final structure (hence short and long end). The next four struts connect to the long ends, and introduce the second rule of building tensegrities with TATT:
When viewed from the front, the two struts connecting to the tendon of a toolkit element, arrive from opposing sides.

The pattern for the second stage

The long end of the new connection connects to the nearest strut of the corner.

Two struts of the second level

The next strut follows the same idea: Connecting to the open long end of a corner strut, having the long end connected to the next corner strut.

Three struts of the second level

Connect the third strut, remember that tendons go outside, the knots point to the short end, struts connecting the same tendon come from opposite directions.

Eight struts of the octahedron connected

After connecting the second level of the octahedron, the structure slightly bends itself into shape. To get the final shape, more bending needs to be done for the final shape. Eight unconnected ends and eight spaces in tendons remain for the last few connections to be made.

Corner with second level turned around next to top corner 

After turning the eight stick module around, the top corner finishes the build.

First connection of the top corner

The first connection comes easy.

Second connection of the top corner

The second connection bends the model into a skewed shape, it follows the same pattern as before.

Three connection of the top corner

The tension increases while the connections aren't balanced, yet the model get more bounciness and stability during the final steps.

Model with four missing connections

The open ends of the top corner now connect to the rest of the structure, with four attachment spots remaining. The four remaining open ends (from the eight struts of the first build phase) connect into this open spots.

Three missing connections 

The same rules as before apply. The knots point towards the short ends, struts connect from opposing directions to a shared tendon.

Two missing connections

Due to the increased tension, unsecured connection might easily slip during this phase.

One step away from finishing

The increased tension makes building a bit trickier. At the same time, the tension guides you towards making the 'right connections'.

Tensegrity octahedron balancing on a corner

Once we last connection is made, you can test the symmetry by balancing the model on each of its six corners

Flattened model

The elasticity of the cords allows the model to squeeze down, the size of the squared loops in the corners determines to flat the model can get. You can adjust the model by reattaching one stick at a time in a more symmetrical way.

Don't take the rules for the build as eternal truth, for other models other rules (although similar) apply. There's more than one way of building any tensegrity structure, only experimentation can improve any construction method.

The Affordable Tensegrity Toolkit just has hatched and needs now good documentation. Please contact me via this blog if you're interested in more details, or have specific requests or comments.