Since a lot of people who are interested in polyphasic sleep are curious about the diet/physical health aspect, I'll talk about my own experiences with that some.
I haven't felt a need to increase my food intake any since I started polyphasing, and this surprised me. However, I have been drinking more water and tea while on this schedule. I usually keep a drink with me at home and have some of it occasionally. With more time spent awake, I'm sure that I'm getting more to drink this way. I haven't had any days when I've felt dehydrated. Previously, when I've had days where I stayed awake longer than 20 hours and then had a long sleep period after, I'd sometimes wake up feeling dehydrated and maybe having a headache after 8+ hours of sleep. When I'm not sleeping any more than 3 hours at a time, I haven't been experiencing this.
I haven't been any hungrier or thirstier, and ingesting more liquid just seems to be a result of spending more hours awake while sipping some water/tea. I still don't eat much at night, and never have, even when I've stayed up most of the night in the past. I have breakfast, lunch, and dinner, and one or two snacks a day. It's rare that I have a snack after dinner. I know some people experience more hunger when they're awake more, or feel driven to eat to keep themselves awake when they're fighting sleep deprivation. That doesn't really ever happen to me. I typically don't become hungry between dinner and breakfast. The way I'd describe it is that my digestive system seems to go to sleep at night, a few hours before my typical sleep time, and it takes a while to wake up in the morning. The earliest I eat breakfast is about 6:00.
Actually, the previous description is probably inaccurate. What is most likely going on is that my hunger follows a circadian rhythm, and I've never developed a need to eat at night. I'm usually doing low-energy activities when I first wake up, too. When I take my nap just before lunch, I wake up hungry. So sleeping itself has no effect, it's the time of day.
There are different reports about how polyphasic sleep affects weight and stress hormones that might contribute to weight gain. Some seem to report experiencing release of these stress hormones from sleep deprivation, and having associated increase in appetite and weight gain. I haven't experienced that, so I would say that's a good indication that I haven't felt much sleep deprivation so far. I've actually lost some weight, but it's <5 pounds, such a small amount that I can't say for certain whether it's connected to the polyphasic sleeping or not. Lots of things can cause minor fluctuations in weight. Some report losing weight with polyphasic sleep due to expending more calories since they're awake more, and I'd say that's a possibility.
I definitely don't think I'm getting any increase in stress hormones. In fact, I would say that I've been more relaxed due to having a sleep schedule that I'm happy with and that, so far, I haven't had many problems keeping. Probably having some more time awake during the peaceful nighttime hours helps as well.
I haven't intentionally changed my diet any while changing my sleep schedule, and I haven't noticed a difference in what I want to eat, either. I briefly covered how I typically eat in my "about" section. Basically, I'm an omnivore (I have some of everything), but I try to keep my diet natural and avoid eating chemical preservatives and refined sugar. I eat a lot of dairy, vegetables, fruit, and white meat. I haven't intentionally eaten beef in about 12 years, since I first heard about madcow disease. That made me aware of how badly beef cattle were treated, the bad diet they're fed, and the sloppy butchering process that was contaminating meat. It also made me realize that I do believe in respecting cows for providing us with milk. I have eaten buffalo and lamb occasionally, as they're said to be healthier red meats, and the animals are supposedly treated better since raising them is not the big industrial operation that raising beef cattle is. That basically covers it. Oh, I also have a little caffeine every day from tea and decaf coffee, usually at breakfast and lunch.
Also, just to avoid confusion and for full disclosure and whatnot, I want to point out that I am female. I have that written on the blog somewhere, but I know that can get overlooked. I think it's cool that the internet is so anonymous that some people couldn't tell, and it's not a big deal to me if anyone assumes I'm male. I just wanted to point it out while talking about physiology here.
That's all I can think of for now.