A Menger Sponge is a self-similar fractal, meaning that its structure is comprised of parts that look like miniature copies of the whole. Its shape can be visualized as follows:
- Start with a cube constructed of 27 smaller cubes
- Remove the center cube and the middle cube of each face to create a Level-1 Menger Sponge
- Perform the steps above n times to create a Level-n Menger Sponge. As n approaches infinity, the fractal object approaches zero volume and infinite surface area, and has a dimension of 2.7268...
In 2006, the Cornell Math Club and a host of helpers built a 5'x5'x5' Level-3 Menger Sponge that resides in Cole Library. The construction required 65,536 pieces of folded paper and about 600 hours of labor (also known as fun).
At right is a computer-generated image of a higher-level Menger Sponge from Wikipedia.