Jerusalem Cube

File:Cube de Jérusalem, itération 3.png

Third iteration

3D-printed model

In mathematics, a Jerusalem Cube is a fractal object created by recursively drilling Greek cross-shaped holes into a cube. The name comes from a face of the cube resembling a Jerusalem cross pattern.

Construction

The construction of the Jerusalem Cube can be described as follows:

1. Start with a cube.
2. Cut a cross through each side of the cube, leaving eight cubes (of rank +1) at the corners of the original cube, as well as twelve smaller cubes (of rank +2) centered on the edges of the original cube between cubes of rank +1.
3. Repeat the process on the cubes of rank 1 and 2.

Each iteration adds eight cubes of rank one and twelve cubes of rank two, a twenty-fold increase. (Similar to the Menger sponge but with two different-sized cubes.) Iterating an infinite number of times results in the Jerusalem Cube.

External links

• Dickau, R.: Jerusalem Cube Further discussion.