Just another Rainbow model D (I believe), but with a floor polisher attachment that utilizes the motor like the Fairfax! Needless to say I've never seen one with this attachment on eBay before.
That's called a Polichamp. We used to sell them back in the 60's and '70's. It was an excellent floor polisher, and built a whole lot better than Fairfax's polisher, which was a friction drive - the rotating shaft extending from the motor rubbed on a rubber ring on the outside edge of the brush. The Rainbow unit used a geared belt (like an Electrolux Power Nozzle belt) from the underside of the shaft which made a friction connection to the separator screw - to a plastic gear, which meshed with teeth on the inside of the metal drum to which be brushes attached. There were polishing, scrubbing, and shampooing brushes. The downfall of this unit was that as kitchen carpet became more popular in the '70's the market for floor polishers virtually disappeared. In order for the unit to turn, when used as a shampooer, the carpet had to be excessively wet (not a good thing, although the Rainbow would extract the moisture) or the teeth on the plastic gear would strip off. Rexair didn't make the Polichamp, they had someone else (I don't know who) make it for them, and the replacement gears quickly became unavailable. Hence a lot of Polichamps went by the wayside.
This is an attachment called the Rainbow Polichamp. I had one on our old model D Rexair. They work very well, but the gear eventually stripped on ours when I tried to use it on the rug to scrub in Capture carpet cleaning granules. It was meant for floors only, not rugs.
I did once use it to polish the floor with paste wax. It brought the floor up to a beautiful shine. The separator nut sits against a little rubber boot and as the motor revolves, it spins the brush in the Polichamp. I haven't seen one in years, they were sold with vacs from the late '60's and early 70's.