This week I rounded up several of my colleagues at the Max Planck Institute for Mathematics for a night of mathematically inspired paper crafts from the website cutoutfoldup.com. The website site features an impressive collection of “interesting things to make out of paper,” and lots of them are mathematical. And while we won’t be setting up an Etsy shop anytime soon — I think perhaps we’re better at math than paper crafts — we did have fun experimenting.

The first one we tried was Dudeney’s classical construction of a square from an equilateral triangle. This one wasn’t too difficult (only one star out of five), and the result was a really fun hinged square/triangle. You can see a video of our completed construction here.

We also tried (to mildly mixed results, as you can see the the header photo above) to cut out an angelfish with one straight cut. Ideally, an angelfish would be obtained by folding a single sheet of paper in just the right way, and administering precisely one straight cut. Ours have a a bit of extra, erm, character. But actually, the anglefish itself isn’t particularly special. Any figure drawn from straight lines can be achieved in this way. Erik Demaine gives a good history of the mathematical properties of this problem on his website.

The hyperbolic paraboloid, which Emily Norton constructed out of a Wheatabix box and some colored yarn, turned out very beautifully. By building up some tension on the cardboard she made a perfect saddle point. It is really cool when you realize this shape with such a *particular* curvature is constructed entirely out of straight lines.

By far the most difficult, and most impressive was the rhombic spirallohedron. This is a polyhedra composed entirely of rhombic faces. You can see it in motion here, it would make a really nice piece of hanging art. Actually, I feel like polyhedra are having a bit of a moment right now. I’ve been seeing polyhedra all over the design scene, like here and here.

Now I really want to build the geodesic dome (large enough to sit inside!) out of newspaper. And then I want to sit inside my geodesic dome and construct this torus. Who’s with me?

Check out these math blogs too: Scientific Kirigami, “Dr. Alan Russell leads instruction in the art of kirigami during #MakeElon workshop, and Quarto Knows.