Hmm, I think we're somewhat talking past each other here. Maybe I misunderstood what's meant by "unit cube".
Mea culpa. I simply assumed we're talking about the cube whose vertices are <±1, ±1, ...>, and the sphere of radius 1 whose intersection with the coordinates axes are <±1, 0, 0, ...>, <0, ±1, 0, ...>, etc.. I guess that wasn't what we were talking about, sorry for the confusion.