Image of the US Capitol Building dome through the trees. The Capitol Building is the heart of the Federal District of Columbia. Although not in the geographic center of DC, Capitol Hill is the origination point for the street grid and the 4 quadrants that define the city. It is also the seat of the US federal government. The building was completed in 1800 with the dome dome being constructed from 1855 to 1866. Currently the dome is scaffolded for a restoration project due for completion by 2017.