Menger Sponge

I'm supposed to be revising for my final year exams, and the Rubik's Cube isn't enough of a distraction, apparently, so I've taken up the crafty mathsy hobby of constructing 3D fractals.

The Menger Sponge is a cube with a hole in the middle, made up of smaller cubes, each with a hole in the middle. Depending on which way you look at it, you either start with a cube and remove the hole, and repeat this forever, or you pick a level of holiness (?) and build it with as many holes as would have been removed by now. Ok, I'm not making sense.

There's not much fun in a level 0 menger sponge - this is simply a cube. But if we consider a cube made up of 3x3 faces, like a Rubik's cube, and remove the centre square from each face, and hollow it out, we get a quite near looking object. That's a stage 1 menger sponge.

The stage 1 is easy and fun to construct from uniform pieces of card, like train tickets or business cards.

The stage 2 (scaled up, where one stage 1 is used as a unit cube in a bigger object) is significantly more work — we go from 20 cubes to 40 cubes, and from 120 cards to 2,400. I built several stage 1 sponges from different types of cards — but didn't have enough to construct a stage 2 in full. So I just stacked them in a pyramid: