Models of the Menger sponge with five iterations. The Menger sponge is a mathematical object, where a cube is successively divided up into 27 sub cubes, which are similarly divided recursively. Each time the centre 7 sub cubes are removed. It is a 3D analogue of the Cantor set, where a line is similarly subdivided. As the iterations approach infinity the object will lose all it's volume, while it's surface area tends towards infinity. It was first described by Karl Menger in 1926, in connection with his study of topological dimension. Computer generated image.