Stellated Icosahedra

You can turn a piece of paper into a sort of puzzle piece in just a few quick folds.  With 6 pieces, you can make a cube.  With 12 pieces or 30 pieces, you can make pointy stars.  (Mathematicians call them stellated icosahedra.)  Making the pieces is simple, and assembling them into these shapes is easier than it looks.

Want to make one? See instructions at the bottom of this post.

What to do with it. All of these are hollow. Once you put one together, it’s easy to get inside by removing a piece or two. You can hide things or use it as the ultimate wrapping paper for smallish gifts. (Girlfriend Approved!)

Larger Assemblies? Are larger designs possible? Of course, larger sheets of paper make bigger stars; I’m talking about building a shape that uses more pieces and has more points. If you assemble a cube and then a 12-piece star and then a 30-piece star, you will see the pattern of how they become larger and more complex. What happens if you try to use even more pieces? After experimenting with more than 100 pieces, I realized that I had a giant sheet of points that never curves to close on itself. It never becomes a ball. Larger stars in this kind of pattern are not possible: the 30-piece design is as grand as it gets.

What does Google think of all this? This is part of the larger world of so-called modular origami. There are many different modules (puzzle pieces) that can build up cool shapes. Michał Kosmulski has a great collection of designs. I don’t see mine there, but his, I think, are generally more intricate.  One uses 210 pieces!

Instructions.

I filmed these videos with an old camera. The video is jittery, but it gets the job done.

How to make a puzzle piece:

Folding 30 pieces took me about one and a half hours. Once you’ve got it down, it’s something to do in front of a book or TV.

How pieces fit together to form a point:

To assemble a piece, just make a point and then build more points off of it. To give you an idea of how it goes, here’s a sped-up video of an entire assembly: