Icosahedron with string

thingiverse

Here's a model to demonstrate a little-known trick of geometry. The vertices of an icosahedron can actually be created using only three rectangles at right angles to each other. What proportion do the rectangles have to have to make it work? Unfortunately, it requires the golden ratio. I must admit that I'm jaded from so many people saying anything slightly larger than another thing is a golden ratio, and when I see a legitimate usage of it, I'm disappointed. The vertices are strung together with builder's cord, and it's quite fun to wind it on. There are holes for a cable tie that locks the plates in place. I also ended up putting a seam of hot melt glue on the edges to make sure everything stays nice and Cartesian when the cord is tied onto it. Blog post on it is here: https://tinkeringsdotorg.wordpress.com/2018/09/08/icosahedron