Here’s another Origami Creation that I learned how to make at the Math Circle Summer Teacher Training Institute (I swear we did math too, I just like to have something to do while other people are talking!):

It’s a hyperbolic paraboloid encased in a tetrahedron. No glue was used and it stays together really well.

Hyperbolic paraboloid (inside) – 1 sheet of paper, lots of folding, about 20 minutes. Instructions.
Tetrahedron (outside) – 2 sheets of paper (same size as above) cut into thirds, about 30 minutes. Instructions (scroll down a bit – only make one of the tetrahedra in the model of course!).

Both units are pretty simple to make if you are patient and can follow instructions, and it is amazing to me that they fit together so well! The Tetrahedron is a bit harder because it’s tricky to fit together. Both units have really cool derivatives and variations that you can make, so they are worth learning how to make!