Tornado

 Tornado, by Francis Ow and David Petty.  Instructions online.

I've previously shown a couple examples of "planar models" of origami.  I still have a handful more.  But this model is different.  It's a pseudo-planar model.

The thing about the planes in this model.  If you follow one of these "planes" around in a circle, you arrive in a different place than you started.  And if you keep on going round and round, you will have covered the entire model.

I drew a diagram of this model, way back.  Check it out!

Later I found a small error in this image.  Can you find it?

The diagram is probably difficult to understand without having the hands-on experience of actually creating a planar model.  Each line represents a "plane".  When two lines cross each other, that represents an intersection of the two planes.  But in a real planar model, each line is a circle, eventually reaching back to its original location.  Here, the planes don't go in circles, but go in spirals.

The other thing to notice about the diagram is that it's based on a particular polyhedron, but it's a rather irregular polyhedron.  This polyhedron has 8 triangle faces, and 10 quadrilateral faces.  That's not a regular polyhedron at all.  It's some sort of... well they aren't even regular triangles or quadrilaterals!  The polyhedron is pretty chaotic, not gonna lie.  But the chaos is beautiful.