©Pat Ashforth & Steve Plummer 2016

©Pat Ashforth & Steve Plummer 2017

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MENGER SPONGE Return to Illusion Art  Buy the pattern on the Illusions page of the Order Form  See Sizes of Knitted Panels    For more information, to view photos of completed projects, and to buy the pattern, go to

The Menger Sponge was first described by Karl Menger in 1926. It is a 3D fractal. Theoretically it has an infinite surface and zero volume.


Take a 3 x 3 x 3 cube and remove the centre cube from each face and the very centre cube. You are left with 20 cubes. From each of these remove the centre cubes as before then keep on repeating this process. The surface area of the remaining  shape keeps getting bigger and the volume keeps getting smaller.