There is no research, just prior knowledge in this post.

I've heard that the human body needs 2 complete R.E.M. cycles in ~24 hours. Generally most of us get 2 R.E.M. cycles per 6 - 8 hours of sleep.

I don't think it's possible to get a R.E.M. cycle in under ~3 hours. The sleep process occurs in stages, and the deep sleep required to achieve R.E.M. takes time.

I know a number of people who claim to only sleep 5 hours a night. The thing they don't claim is that they sleep in on the weekends for about 3 - 4 hours each day.

The point is that you have willpower and you can push yourself beyond your normal running parameters, but eventually, your body will get what it needs.

Also, naps make me cranky and more tired than before I took them, so I'm perfectly biased against any theory that promotes napping.