High Quality Content by WIKIPEDIA articles! In mathematics, the Menger sponge is a fractal curve. It is a universal curve, in that it has topological dimension one, and any other curve (more precisely: any compact metric space of topological dimension 1) is homeomorphic to some subset of it. It is sometimes called the Menger-Sierpinski sponge or the Sierpinski sponge. It is a three-dimensional extension of the Cantor set and Sierpinski carpet. It was first described by Karl Menger (1926) while exploring the concept of topological dimension.