The Menger sponge is a fractal object that has any number of interesting mathematical properties and one unexpected and very attractive physical property, which George Hartexplored in a video and a page on his website.
There have been a number of Menger sponges on Thingiverse, including one set up to show the diagonal cut that Prof. Hart discusses. I could never get that part to slice correctly, so I made my own in OpenSCAD. That said, my second-order version gave Slic3r some problems as well, so I've also included the STL after being fixed by Netfabb Cloud. For either first or second-order, you'll need two copies to make a full cube.