Here's a model to demonstrate a little known trick of geometry. The verticies 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? (sigh) The golden ratio.
(I must be jaded from so many people saying anything that's slightly-larger-than another thing is a golden ratio, that when I actually see a legitimate usage of it I'm disappointed)
The verticies are strung together with builder's cord and it's quite fun to wind it on.
There are holes for a cable tie, which 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 on it.
Blog post on it is here: