I looked into this a long time ago, and from everything I found it seemed like the polyphasic (short nap only) sleep schedule is unsustainable. I don't feel like looking around for references, but here are highlights of what I learned about sleep:

1. How much sleep you need varies from person to person -- some people need 6 hours a day, some need 10. The average is about 8.
2. More important than how much sleep you need is the quality of the sleep you get. The link from OP is right, REM sleep is important, but I don't think you can ignore the other parts (if the full sleep cycle wasn't needed, why didn't evolution eliminate it from some species? That would be a huge advantage).
3. A full sleep cycle varies by person, but on average it's about 90 minutes (give or take 30 minutes). REM occurs at the end of each sleep cycle. Pay attention to the time when you wake up in the middle of the night -- you can easily figure out your own cycle length (mine is right about 90 minutes).
4. Short naps are good for temporarily restoring energy/alertness, but they do not catch you up on your sleep. The "siesta" sleep pattern in the OP link won't work well long-term because you're cheating your body out of a sleep cycle each day. That will catch up to you in a few days. Also, calling it a "siesta" is bullshit -- in countries that use siestas (Spain, Italy, Greece, etc.) they set aside about 2 hours for mid-day sleeping.
5. It's a bad idea to take a nap longer than about 30-45 minutes but shorter than your normal sleep cycle. You will wake up feeling very groggy (it's called sleep inertia) and you wouldn't have had a full restorative sleep cycle.

About the polyphasic sleep in the OP: it was a pattern designed by a ship captain that was trying to make a long voyage by himself (crossing the Atlantic, maybe?). In general, that sleep pattern is useful for long periods where you need to stay awake but you do not need to be mentally sharp (your mind will not operate anywhere near normal waking levels). It is not meant to be a sleep pattern for normal life.

FYI, I stick to the traditional siesta sleep schedule (aka biphasic sleep). It's pretty simple -- I sleep about 6 hours at night and I take a 1.5 hour nap after work (working from home makes that very easy). I get a total of 7.5 hours of sleep per day and I'm pretty much always alert and awake. And since I started doing that (about 8 years ago) I find that I usually wake up before my alarm, something I never used to be able to do.

One last comment (wow, this is long already). If you can, you should schedule your sleep to be in multiples of your sleep cycle. I always plan my sleep that way now. Being interrupted in the middle of your sleep cycle causes sleep inertia, making your morning very tough. Plus it's just a waste of your time -- if your alarm goes off 45 minutes into your sleep cycle, your body doesn't count those 45 minutes as restorative sleep -- you might as well have woken up 45 minutes earlier (and felt more alert when you woke up).