Saving Face

http://commons.wikimedia.org/wiki/File:Geomagic_square_-_Joker.jpg
Image: Wikimedia Commons

“The Joker,” a picture-preserving geomagic square by Lee Sallows. The 16 pieces can be assembled in varying groups of 4 to produce the same picture in 16 different ways, without rotation or reflection.

The outline need not be a joker — it can take almost any shape.