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.)
