Yes, you can be fully rested with much less than that actually, according to polyphasic sleep theory.

The problem is that you have to sleep multiple times in a 24-hour cycle. The simplest version is the biphasic pattern or "siesta", where you take a nap in the middle of the day, as was traditionally done in Spanish cultures. The more extreme versions involve brief sleep periods evenly spaced out during the 24-hour cycle.

As should be obvious, the problem with this is that our culture doesn't permit it. Good luck finding a job that'll let you take a 1-hour nap in the middle of the workday (in addition to your lunchtime).

It depends on the kind of work you do and on your boss. I think people working in software companies have great freedom in their time management and can easily extend the lunchtime to get a nap after lunch.