Tensegrity structures are objects which incorporate tension and compression elements into a sturdy, flexible structure. Much has been written about them which you can read about elsewhere. If you're here, you probably have some notion of what a tensegrity structure is, even if it's only from the photo.
Note: This instructable is based on construction techniques developed by Les Tanner at the College of Idaho. His technique is more refined but requires specialized equipment. You can read more in this 2018 article.
Here, we use a stripped-down version of Les's approach to build a tensegrity icosahedron.
Depending on what you have around the house, your ornament should cost from $0 to $3 to construct.
Step 1: Materials and Tools
2 sturdy, straight bamboo skewers (10 inch)
1 Popsicle stick
1 spool of thread
1 razor blade or Xacto knife
Ruler or measuring tape
Wire cutters or alternative (see next step)
Step 2: Cut Your Struts
Bamboo skewers within a pack vary in their thickness and sturdiness. Choose two that are especially thick and straight.
Starting at the unpointed end, measure and mark three-inch segments. You should end up with three segments of three inches each, plus a one-inch pointed end.
Using the wire cutters*, cut off the pointed end and discard it.
Cut along the remaining segments to create your three struts.
Repeat with the other skewer for a total of six struts.
If you want colored struts, paint them now. Otherwise, leave them with their natural finish and continue to the next step.
*Sturdy wire cutters work well for this, but you can also use heavy scissors or a fine hacksaw. If you must break it with your fingers, try to score the skewer first with your razor blade and sand the rough edge flat after snapping.
Step 3: Make Your String Template.
Cut the rounded end off your Popsicle stick so that it's flat.
Measure 7/8 inch and cut again. You should now have a rectangular piece of wood that is 7/8 long.
Step 4: Slot Your Strut
Place the edge of your razor blade against the flat end of one of your struts. Carefully push it into the strut to a depth of ~1/4 inch, creating a thin slot in the end of the strut.
Now, slide the end of your string into the slot. The slot should be narrow enough to pinch the string and hold it in place.
Wrap the string around the strut 2.5 times and then run it through the slot again. The long end of the string should now be sticking out of the opposite side as the short end.
Step 5: String Your Strut
A. Slot the opposite side of the strut at the same angle and depth as before.
B. Run the long end of your string into the slot, leaving a little slack between the two ends. Do not wrap the string yet.
C. Now, use your template to determine the correct length of string between the two ends. Do this by propping your template up at a right angle so as to create a gap of 7/8 inch between the middle of the string and the middle of the strut. Your string is now the correct length.
D. Now, wrap the string around the end of the strut 2.5 times, just as before, sliding the long end into the slot a second time.
Repeat B, C, and D so as to connect the thread back to the end where it started. Wrap 2.5 times again to complete, and cut the remaining thread.
Repeat all steps so as to create six identical struts with strings.
Step 6: Connect the First Three Struts to Each Other
Choose one strut as the "primary strut." (In the first photo, this is the horizontal one in the center.)
Slide one of the strings of a second strut into one end of the primary strut.
Slide one of the strings of a third strut through the other end of the primary strut.
Your three struts should look like the image, with one thread of each vertical strut threaded into each end of the horizontal strut.
Step 7: Connect the Fourth Strut
Lift your primary strut by its middle to allow the unconnected strings of the other two struts to dangle.
You will now need to connect a fourth strut to those two dangling strings.
You can do this either by having a helper continue to hold up the primary strut while you connect the fourth strut, or, you can carefully turn the assembly over, keeping track of the two loose strings, and connect them on a tabletop (as pictured).
Step 8: Connect the Fifth Strut
The assembly gets a little complex at this point. However, you can overcome this by... not giving up! Study the photos of the completed icosahedron tensegrity and compare it to what you've got, making changes as needed.
Your primary strut and its parallel strut now each have two pairs of dangling strings. You will now need to connect these two pairs of remaining strings to the ends of the two remaining struts. You will additionally need to connect the strings of those struts (the fifth and six, that is) to their adjacent struts.
To connect the fifth strut, select which side of the primary strut the fifth will connect to. (In the photo, it is being connected to the far side.) Slip the primary strut's far side string into one end of the fifth strut, and the far side string of the fourth strut (that's the one parallel to the primary strut) into the other end of the fifth strut.
You can use a helper for this step, or do it carefully on a table top. Personally, I like to confine the frustration to just one person, as I find it easier to manage that way.
Step 9: Connect the Sixth Strut
By now, it should be obvious that the sixth strut connects to the two remaining strings.
Do this the same way as you did the fifth strut, but on the closer side of the primary strut instead of the far side.
Finally, connect the sixth strut's strings into the ends of their adjacent struts.
This is, without a doubt, the linchpin of this process. It may require several tries. Don't feel bad if your assembly falls apart multiple times as you connect the fifth strut. You might even find that the building tension in the string sends one or more struts flying across the room. Keep trying!
You might also worry that your threads will snap. If you measured your strings correctly using the template, this is very unlikely. You will be surprised how much tension this assembly can handle.
Step 10: Straighten the Struts
Congratulations! You should now have a completed, if somewhat wonky, icosahedron tensegrity structure!
Straighten the elements by grasping adjacent, perpendicular struts and moving them so they form perfect right angles with each other. Sometimes, this will pull other struts out of alignment, so it can be helpful (though not essential) to have another set of hands to help with this.
Keep going around the structure doing this to any pair of perpendicular elements that look uneven. Shoot for "pretty close", rather than absolute perfection.
Step 11: Complete
Tie small piece of string, ribbon, or wire into the structure as a hanger.
Hang on your tree!