Un-Tied or Tied-Up Armchair?

Un-tied or tied-up chair?
Found this armchair with Tie Covering by Peter Rafael Russo on a blog of SF Weekly. The chair was entered for a 2009 “Masterminds” design competition which in one way or the other was organized by Stanford University.

As we have our typical language problems by nature of our non native English speaking contributors already, my question is: Is “Un-Tied” better than “Tied-Up”?