This is of course anecdotal, but a few years back I did the polyphasic experience, and I can confirm that dreaming consistently occurs during those 20 minute naps, which strongly suggests REM sleep. In fact, those dreams were some of the best and most vivid dreams I've ever had, presumably because you're never more than 20 minutes away from consciousness, so you remember the dreams clearly, and the dreams are strongly correlated to your mental state going into the nap.

Everyone should try the polyphasic experience for at least a few months of one's life. It radically alters the way you think about time.