No way can a group function as a team if they never have any face to face time. I was, and still am, a firm proponent of this. Fixed schedules are better than fluctuating. People need some stability to arrange their lives around. To do 7x24 comfortably, you'll need 12 people and a supervisor.
People get three days off in a row, including one weekend day.
The only ones who are left out are the overnight crew. This is based upon nine years of operations center experience.