The ancillary dome-like structure on top of the building is known as a CHUTTRI, an integral part of Indian architectural design.

Shot at Indian President's House @ Delhi 

The dome in the middle involved a mixture of Indian and British styles. In the center was a tall copper dome surmounted on top of a drum, which stands out from the rest of the building, due to its height. The dome is exactly in the middle of the diagonals between the four corners of the building. The dome is more than twice the height of the rest of the building.