This is a derivative of the apparently impossible cube puzzle. While a Cube is cool a sphere is much cooler. I take no credit for the original design from which this was derived.
I didn't have to original model used so I grabbed the impossible cube STLs and unioned them with a sphere (as appropriate).
Print two "s1" parts and two "s2" parts on your well calibrated 3d printer. (I printed in .3 height 10% infill on my ToM)
You may need to clean up any little blobs.
This solves the same way as the cube it's a little harder due to not being able to set it on a flat surface.
I recommend scaling this up a little bit after printing it myself. Unless you have tiny hands it's challenge to put together at the size posted.
Check ou derivative: http://www.thingiverse.com/thing:25395 - Open Scad Source (works w/ cube and sphere). It fits together a little tighter and as a result is a little more fiddly to put together. If your printer isn't well calibrated print mine LOL.