I don't want to sugar coat anything in this article, so let me start by saying that polyphasic adaptation is not a pleasant process. It can be a very interesting and enlightening process ( I certainly found it to be), and I can honestly say that it is a simple process, both in the underlying principles and in practice. But not pleasant...never pleasant.
It isn't pleasant for one very fundamental reason; namely that the whole process relies on making you so tired that your body has no option but to adapt to the new sleeping schedule in order to survive. Sound nasty? It is. Before I started this process I had no idea what I was letting myself in for...and that was after I had read everything I could on the subject of polyphasic sleeping. Trust me, if there was some online or printed material about the Uberman, I had read it. I took a full two months to research this topic before I tried it, and I was manically iinterested for the entire time.
What I found out was that sleeping for eight hours a night (I normally needed nine or 10) is not necessarily optimal. We do normally sleep for around eight hours a night, and in these eight hours we will go through five stages of sleep. These levels range from light sleep (stage 1) to deep sleep (stage 3 / 4), and dreaming or REM sleep (stage 5). Scientific opinion seems to be fairly divided when it comes to what actually happens when we sleep, but most seem to agree that we require dreaming sleep (stage 5) in order to function. Given my experience in polyphasic sleeping, I would say that stage 5 sleep is the key to feeling rested when you wake up.
One of the key things you will find when adapting to polyphasic schedules, is that your body will change the way in which it uses the time you give it to sleep. To start with, it will be expecting eight hours of sleep, so when you nap, your body will be in no rush to start dreaming. You then wake up after 20 minutes or so, and feel like death. Slowly though, your body realizes it has to optimize the use of the sleep you give it, and you start to dream almost instantly upon going to sleep.