It's like 'applicable origami':  Hexaflexagons.  Fold them up and invert them, time and time again, and then discover something about them, and then invert them again and again.  An amazing video (it's too fast for me to keep up enough tolearn how to make one, but an entertaining video nonetheless).

If you know how to make one of these, and you have the patience to teach a half-brained dimwit like me,
email me
and we'll get to folding!

 

(Via Youtube)