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polyphasic sleep
I've tried it, or something like it, but it is not sustainable in my eyes.
Steve Pavlina did it for a while, and wrote about it, but even he eventually went back to a normal sleep schedule.
I immediately thought of that article when I read the original post here!
Any time you're making changes to your sleep schedule, the first week or two will be be miserable. Your body will, at the sacrifice of the other cycles, adapt to shift into REM faster and faster if you're becoming sleep deprived.
Most of the time, people are asking the opposite question that the OP is asking, so I think this is an interesting topic. I've had some sleep issues and for the first part of this year I was on a 32/8 sleep schedule because it was the only way I could fall asleep, absent some kind of pharmaceutical. Before that, I was sleeping around 4-6 hours per night and during both of those times I functioned approximately the same.
For comparisons sake, I've felt and functioned CONSIDERABLY better the last several weeks, due to getting 6-8 hours of sleep per night. REM takes precedence in terms of priority, but NREM (especially stage 3 slow-wave sleep) is also very important in determining how you feel.
Long story short I think one can
survive on a really diverse set of sleep schedules, but how well that works out for you in a practical sense can vary. I remember reading in neurology that certain species of birds who fly great distances over water actually slip in and out of REM between wingbeats, and the accumulation of these disjointed seconds of REM satisfies their needs during long-term flights where landing isn't an option (as a disclaimer this theory is still controversial as its difficult to strap an EEG machine on a bird mid flight

)