What is the Zero Density Cube?

[chaotixmonjuish]

I may be posting this in the wrong section:

A while ago I was reading a collection of articles on Wikipedia and I stumbled upon this article that was pretty interesting. It was about a cube, on each face of the cube a small cube is cut out. It is done many more times. The next thing I recall was that the figure had a density of 1 or 0. I'm not sure what this is called. Does anyone have any idea about this?

 

[HallsofIvy]

Sounds to me like your are talking about a "Sierpinski sponge". Divide a cube into 27 small cubes by cutting each face with two planes and remove the middle cube. Now do the same with each of the remaining cubes. It has fractal dimension.

 

[Cexy]

I might be describing the same thing as HofI, but the Menger sponge is constructed in much the same way except that you also remove the centre cube, so that you're left with 20 smaller cubes. Iterating this infinitely produces the Menger sponge, which has infinite surface area and zero volume.

 

[chaotixmonjuish]

It was the first one, but the second one seems pretty similar