This weekend I built a Tensegrity structure as a demonstration of principles of balancing tension and compression in structures for my course RBT379 - Mechatronics. I've been fascinated by the aesthetic of these structures - all triangles and edges, but somehow magical as your brain tries to wrap itself around the reasons why the solid supports seem to be floating in air, and the structure is still standing.
I found a couple of excellent pages documenting how the structures work and are assembled - one from the artist Kenneth Snelson explaining the aesthetic inspiration for Tensegrity structures as a kind of 3-dimensional weaving, and another more practical site detailing the construction of a Tensegrity coffee table.
I used the UAT 3D printer to make 12 struts. You can make these out of much simpler materials (wood, copper, chopsticks, etc), but the Inventor Part design for the struts are provided here. A gallery of the build process and completed 3-level structure (and one rubber-band version) are below.
I used 20lb test mono-filament fishing line and 2 sets of good smooth-jaw pliers to tie the knots (grip-jaw pliers scar the fishing line, causing breaks after you've carefully tied many little knots), following the guidelines at the Tensegrity coffee table website. If you do this yourself, construct a jig that will allow you to accurately create the tension links at a certain distance (the length of your struts divided by 1.4).
I built 3 modules, 2 "left-handed" and 1 "right-handed." To assemble them into the tower, I hooked the struts of one module into the base triangle of tension elements of another, forcing the base triangle into a hexagon.
The resulting structure is surprisingly sturdy, and the fishing line is somewhat transparent, adding to the mystical effect I was trying to emphasize.