Jerusalem Cube

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Third iteration

In mathematics, a Jerusalem Cube is a fractal object created by recursively drilling Greek cross-shaped holes into a cube.[1] The name comes from a face of the cube resembling a Jerusalem cross pattern.

Construction[edit]

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.

References[edit]

  1. ^ Eric Baird (2011-08-18). "The Jerusalem Cube". Alt.Fractals. Retrieved 2013-03-13. 

External links[edit]