Hi Dan:
The Dyson DC-31 handheld that I have came with a kit of attachments, and one of them is a six-inch-wide "rectangular horn" for vacuuming hard floors. Around the perimeter of this "horn" is that same red velvet-ish directional material used on lint wands, where if you wipe in one direction, it picks up the lint; in the other direction the lint is removed.
Their website doesn't seem to show this attachment. Look toward the bottom of this page and take a look, if you would. Are any of those attachments what you are talking about?
http://www.dyson.com/vacuums/handhelds/dc34/dc34/specifications.aspx