The Menger Sponge

Start with a cube, divide it like a Rubik's cube into 27 smaller cubes and remove each central cube to leave 20. Recursively apply this procedure to each of the remaining cubes and you will have successive levels of Menger's sponge, a recursive 3D shape generalizing the Sierpinski carpet—in fact each face of the Menger sponge is a Sierpinski carpet. This Demonstration provides four variations on this idea, starting with the Sierpinski carpet.

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