Menger sponge with external support

The [Menger sponge] is quite difficult to print on a standard filament-based 3D printer; it's full of overhangs. Internal support won't work because it can't be removed, which leaves nice Menger sponge prints in the domain of other 3D printing technologies.

[Menger sponge]: http://en.wikipedia.org/wiki/Menger_sponge

On the other hand, the shape prints just great on the diagonal, as a few people [have noted]. That means it would be possible to print a sponge on the [diagonal] and glue the halves together, but that seems like cheating.

[diagonal]: http://www.thingiverse.com/thing:234989
[have noted]: http://makerhome.blogspot.com/2014/01/day-155-menger-slice.html

If you could print the sponge standing on a corner that would be fine, but it would certainly fall over within a few layers. I tried a couple of times to use automatically generated support from different software packages, but they all insisted on trying to support the interior holes that don't need it. Then I wa