I would categorize the “Batman” Cartwheel in the “Even More Challenging Projects” section, not because of the complexity of the shapes, which are very straight-forward, but because of the sheer number of the pieces and the difficulty of keeping each piece in the proper order when they look so much alike. It can be a challenge to cut multiple pieces of the same shape and make them all exactly the same, so it is important to keep each piece in the correct location.

Click on the picture to enlarge the image. It is referred to as the “Batman” because of the bat-like shape at the center.

This pattern is based on Penrose Tilings. (see the Penrose Rhombi pattern for another example of this.)  As I mentioned in that post: Penrose Tilings have a number of astonishing properties. One is that any finite portion of any tiling is contained an infinite number of times in every other tiling. This means that you cannot tell, by examining a piece of a tiling, which pattern you are on!

For more information on Penrose tilings see Roger Penrose’s book The Emperor’s New Mind: Concerning Computers, Minds, and the Laws of Physics

or see the illuminating article on Penrose Tilings by Steven Dutch of the Univ. of Wisconsin in Green Bay.

Good luck with this piece!

View the “Batman” Cartwheel pattern in black and white jpg
download the GlassEye pattern