Trapped in a Menger Sponge

Saw something amusing today on a math blog. Under the heading of "weird things math/CS/physical science students build," this entry from the Cornell math club:

"Math Happens"

It's a Menger sponge, an object like a Sierpinski carpet, but in dimension 3 and with cubes, (he said like that instantly explained everything). You start with a big, solid cube and divide it into a 3-by-3-by-3 grid of smaller cubes. Then you knock out the centre piece of each face and the centre piece of the whole thing, leaving 20 pieces left, like a cube with a jack hollowed out in the middle. Repeat with each remaining piece, "ad infinitum," as they say. The Menger sponge is the limit of this process (more precisely, the intersection of the intermediary constructions). It has the really cool property that every curve (topological space of [Lebesgue covering] dimension one) embeds homeomorphically into the sponge, according to the Wiki article, making it a universal object for (these, topological) curves.

Needless to say, the first thing that flashed through my mind was half a script and the byline for Cube 3. One small problem: the thing is Lebesgue null. On the other hand, the reasonably high Hausdorff dimension (about 2.73) suggests something can be worked out, either by holding our noses and going or switching to the four-dimensional analogue.

I'm afraid the ol' UBC Math Club hasn't constructed anything quite so, well, intimidating. There's just this fun guy:

Pumpy the Irrational Pumpkin

I can't recall seeing any curiously intriguing math-themed objects at Princeton, although I haven't been keeping my eyes open. It's more of a tigers-and-abstract-statuary sort of place. Next time I'm there I'll snap a shot of the bust of David Hilbert in the common room.