Mathematical Origami

This is not origami.

It should probably be noted somewhere that this is more "papercraft" than "origami", and the thing you download is just the net of the solid, not instructions to make what's in the picture.

Also saddened by the lack of Catalan solids

I was lucky enough to meet the guy behind mathigon for dinner a long time ago. He's brilliant! I'm always excited to see what he is up to! Glad to see this voted up.