First of all, the term "heavy" refers to an aircraft's weight, if a plane weighs a lot, it is referred to as a "heavy".
I believe you are refering to the "relief crew". The relief crew are just that. When the first group of pilots fulfill their time in the cockpit, the relief crew will take over. They consist of totally new captains, first officers, and flight engineers.
Yeah, I remember hearing about the ATL-HNL flight. The last I heard, they have a "technical stop" in LAX in order to change crews.
Since ATL-HNL is a long flight, you obviously need a relief crew, but I don't remember what was so special about this flight. When I flew ATL-LGW a 777 (which also had a relief crew), I saw one pilot leave the cockpit and he went to sleep in one of the seats in Business Elite (First Class). However, some pilots and flight attendants go to sleep in bunk beds that are right behind the cockpit I think (there are pictures of them on this site).
I'm sure the pilots can go to sleep in the first class seats, but they may have demanded that they have bunk beds, which the 764 (which is used on the ATL-HNL route) does not have. So, the pilots can demand a technical rest stop then.
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