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).

Watch the sponge's construction

Menger Sponge from WikipediaAt right is a computer-generated image of a higher-level Menger Sponge from Wikipedia.