Sure, the East Meets West isn't really a flying carpet. Styled to accommodate seating for multiple people, however, this sofa's flowing design sure evokes that feeling.
Created by Tonio de Roover, the piece is one part living room furniture and one part sculptural object. The actual seat area looks too protruded for its own good, so it looks more suited to lying down for a nap than sitting down to watch TV. As a whimsical flying carpet in your living room, though, it looks absolutely perfect. Except for the part that it doesn't really fly.
The East Meets West is a 1600 x 1600 x 950 mm (w x d x h) sofa that uses a Persian carpet, laid over a partially-hidden bench, to create the "flying carpet" effect. Actual frame is made out of birch plywood and galvanized steel, with velcro used to bind the rug to the unit. It's pretty clever, aside from looking downright gorgeous.
It appears to be an exhibition build, so don't expect them in your local furniture store anytime soon. If you're up to it, you might be able to make one yourself with a long bench and a nice rug, although, the illusion of flight does seem a bit more difficult to replicate.