The Green Dome in the Village is its most prominent structure. It is the where Number 2 has his or her office and has been referred to as "Number 2's house", with several episodes indicating they also live there (apparently accessing the office by way of an elevator). The Butler also works at the Green Dome, assisting Number 2.
Like most Village structures, what the Green Dome contains is left ambiguous and adjusts depending on a story's needs. In "Once Upon a Time" it is revealed that the Green Dome is located above a large chamber where the "Degree Absolute" procedure is attempted, while "Fall Out" indicated that this chamber was, in turn, connected via another elevator to a large underground cavern containing a rocket.