It may be a fun thing to try but I'm sure everybody having actually done it wouldn't recommend it (same goes for most doctors I guess).
This is an interesting idea. Are there any examples of people keeping up such a sleep schedule for a prolonged amount of time? Wikipedia only mentions Buckminster Fuller. Out of 7 billion people more than 1 should have managed this if it is actually possible.
When I first starting reading the OP, Leonardo da Vinci immediately came to mind. I just Googled it to verify.