Half a Menger Sponge

George W. Hart

This page answers a question posed on my rapid prototyping page: What shape is the cross section when one slices a Menger's sponge in half on a plane which is the perpendicular bisector to the cube's long diagonal?

It is not hard to see that it is a hexagon with some pattern of holes, but the shape and pattern of the holes is surprising. Below is a  photo of the model I made by selective laser sintering:

And a computer rendering, in case it is clearer:

Credit: As far as I know, Sebastien Perez Duarte was the first to pose this puzzle. His computer-rendered image is here.
(And as far as I know, my nylon model shown above is the first physical model of this.)