It should surprise no one that MIT has an origami team whose goal is to create a third level version of a 3D fractal known as a Menger Sponge, whose ultimate incarnation is a shape with zero volume and infinite surface area. Here's how they do it.
Working with business cards and some kids, the team does manage to create an approximation of level three of the fractal, and it looks a lot like some of the architecture on the MIT campus. Because of course it does. Watch this video to learn about the relationship between maths and structural beauty -- and a bunch of heroic fractal lovers.