I've tried polyphasic sleep on a number of occasions over the past couple of decades, with a few different schedules. It doesn't work (for me). Perpetual grogginess becomes the norm, and I always felt tired, occasionally short of breath and prone to heartburn (this one seems weird, but I get heartburn when I'm overly tired in normal circumstances, as well).

The best science I've been able to find on the subject seems to match that experience. Some people can "feel fine" on a polyphasic schedule, but in tests there does seem to be a decline in performance. Slower response times and less accuracy on hand-eye tests, etc. that is similar to the decline experienced by sleep deprived subjects.

I'd love to have several extra hours a day, but from what I can tell, there are trade offs that nullify the productivity and "more time" advantages.