Big kudos to Matt. I thought that it would be a limit of the cube approaching a sphere, but figgured that was too elementary of an answer to give mehtank all the trouble. This is coming from the guy who drove his calculus teacher up the wall by using common sense instead of integrals to do problems (and honestly, she was right
). Even so though, I'm pretty sure that it would be a sphere, assuming that the corners wouldn't break by then.
~Tom Fairchild~, who'll bring it up with his math prof. once school starts back up again.