Read here about tensegrity structures composed of 270 struts, part of a series of pages organized by strut count.
270 Strut Sphere by Leftwich
Jim Leftwich posted details of his 270 strut model to the Well. It was constructed with wooden dowels and nylon thread. The colored hairbands wre added last, as an additional method to hold the nylon tendons in place.
Leftwich wrote, "each strut (270 in this particular sphere) is exactly the same size and configuration, so the first job it simply to make all the struts, with the slot cut at each end, and its tensional element (nylon string) attached. I had made many smaller (12-strut and 30-strut) spheres prior to attempting this big one, so I would urge anyone interested in building tensegrity spheres to do the same. It will familiarize one with the basics of tensegrity construction, which will be very useful in attempting to make larger spheres. The reason I had to experiment with the building of the 270-strut sphere was that unlike the 12-strut and 30-strut spheres, the 270-strut sphere does not have an even geometry of strut-group components around the entire sphere. When I attempted to connect the struts together in only the same six-strut components that I'd used in smaller spheres, I got a warping sheet, instead of a sphere. It was only when I realized through experimentation that the correct pattern was to intersperse 5-strut components throughout the sphere, and that these pulled the whole system into a spherical shape. In my photos, I've used yellow hairbands to highlight the five-strut components, black to highlight the six-strut components, and red for the struts between these. It simply helps to show the overall pattern." 
Detail of his nylon tendon connection method:
Leftwich wrote, "each strut's tensional elements is pulled through the slot at one end, brought over the front of the strut, and pulled through the slot at the other end in the opposite direction. The loose ends are then cut and melted to create a ball that prevents the string from slipping back through the slots." 
Links and References
Jim Leftwich 270 strut page: http://www.well.com/user/jleft/graphix/tensegrity_sphere.html
] Jim Leftwich 270 strut details page: http://www.well.com/user/jleft/graphix/Tensegrity_Sphere_Detail.html