The Menger sponge is a spatial analogue of the Sierpinski carpet. In each iteration, the cube (or each of its subcubes) is decomposed into "27 = 3\cdot 3 \cdot 3" subcubes, and seven of these subcubes are removed (not from the edge, but from the center and the facet centers). Continuing this process hollows out the cube and, after an infinite number of iterations, creates a Menger sponge.

The Menger sponge has the Haussdorff dimension d = ln(20)/ln(3) \approx 2.7268. The volume of the Menger sponge is zero, the surface area is infinite.