The Menger Sponge is a three-dimensional fractal curve; if you have seen the Cantor Set (in one dimension) or the Sierpinski Carpet (in two dimensions), the Menger Sponge will look familiar to you. If you haven’t see those other things then this is a good opportunity to spend some quality time on Wikipedia.
In his book Project Origami, Thomas Hull gives instructions for folding models of portions of the Menger Sponge out of business cards. He also includes this dire warning:
Instructors in any class using this activity should be forewarned that it is normal for students to become addicted to making business card cube structures.
For our final mathematical paper folding project of December, we assembled a Level 1 Menger Sponge model:
This model used up my entire supply of old University of Minnesota business cards; to make the Level 1 sponge we will need another 2,280 business cards. If you have any defective business cards (former institution, old job title) you would like to donate to our cause, please let me know!