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Icosahedron with golden rectangles
Some years ago I read that if you take three golden rectangles, concentric & mutually perpendicular, each piercing one of the others and being pierced by the remaining one, then their 12 vertices are the vertices of a regular icosahedron. This caused me to wonder whether, if the longer sides of the rectangles were rigid rods and all the edges of the icosahedron were cords, the resulting model would keep its shape while hanging from one of the rods -- that is, whether the threads would all be in tension. I did not know any way of figuring this out, so I tried to make one. But that is hard, especially for me, because I no longer have binocular vision. I tried it with wooden skewers, sewing thread, & tape, but only made a mess. I consulted a friend, who is very smart about geometry, and he thought the answer to my question was no, but he also suggested using drinking straws for the rods & threading the threads thru them.  By doing that, after some weeks of intermittent effort, with many mistakes, I managed to make a tolerable model & ascertain that actually did keep its shape under gravity. So now I am thinking of making a pretty model, using yarn instead of thread.

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Don't know if you know this already but this is a type of tensegrity structure.

No, I didn't. One even used to be able to get a kit for it:

Thanks very much.

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