The Triflexagon!

The Triflexaon - what is it??

It starts like this

You then fold it and glue the last flap to form a flat hexagon with 2 faces i.e. front and back.

However, when you flip it, the face on the back comes to the front. (A "face" is a flat side). But when you flip it again, a THIRD face seems to arrive from nowhere! It's very strange, as you'll find out when you make one. Maths magic!