Continuing what I started in December, I finally finished making a stellated icosahedron out of 30 Sonobe units. Each Sonobe unit corresponds to an edge of the icosahedron, and interlocks with three others to give the whole thing a remarkable degree of rigidity, even though it’s made completely out of paper.
Here are the requisite photos, showing first fivefold symmetry:
…threefold symmetry:
…and twofold:
Unlike with the cube and octahedron I made out of Sonobe units, where I just put colors together more or less randomly (only ensuring that no two touching units were the same color), with this icosahedron I very carefully researched a color scheme with some really nice mathematical properties. I’ll explain that in my next post!
The Math Less Traveled 
They are very beautiful, Brent, especially the five-fold.
Can I ask how long it took you to build these (not counting the time to prepare Sonobe cubes)? It looks like a great project that we can lead in a class or at a meeting.
It’s a little hard to know since I made the Sonobe units in parallel with building the icosahedron, as I needed them. But actually I think the majority of time was spent making the Sonobe units. Once you have them it does not take too long to put them together. I think this would indeed make a great group project.
Awesome!
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