I made a compound of 5 tetrahedra out of pool noodles. Noodles are 55" (about 4.5 feet) long with a 2 3/8" diameter. I cut them in half these give a Length/Diameter ratio of 11.5789, which worked out well. I describe the whole process at Pool Noodle Spikey.
I'm using less than half the box, though. For each of the five colors, I'm only using six noodles, each cut in half, to make two 5-tetra compounds. I'm also using 40 connectors. There is a lot of foam friction holding this together now, so a few connectors could be removed. If I hadn't cut these in half and let the noodles extend past each other, I could have used 4 pieces of rope to secure one tetrahedron, and the rest would stay together with friction.
QUESTION -- with a box of 35 pool noodles, what is the most interesting stable mathematical structure that can be built, with the fewest connectors? It's possible to have seven touching cylinders. How many bendy pool noodles can be forced to touch? How many of the 31 great circles can be managed? What are good alternates to 72 pencils? Do Kostick stars work with noodles?
MOTIVATION -- This is intended as a math for kids project. The structure you suggest must be buildable with actual pool noodles. You can use any connectors suitable for a kids project. Cutting noodles is fine (I did it).
