This is the first of several Crease Pattern Challenges in one day (see Challenge 27 here for more info). I didn’t fold them on the same day, just put them here. I think. I’m pretty sure.
This is Challenge 19: A Regular Tetrahedron with a Hyperbolic Paraboloid by Satoshi Kamiya. You may ask, “What is a tetrahedron?” Well, “tetra” means four, and “hedron” means bases or something. “Regular” implies that all the faces are the same and have the same angles when making the polygon. So it’s a pyramid.
That should be boring, but it was made by Satoshi Kamiya. The “hyperbolic paraboloid” is the interesting part. This is essentially a saddle-shaped surface, and he put it in the center of the square to cause it to fold in to the tetrahedron. Here it is pulled out and collapsing back.
While it initially looks boring, it’s pretty interesting and a little trippy.