The principal structure of the
church is an
octangular building, which was built by
Crusaders (there are no significant remains of previous buildings). Echoes of this form can be found in many parts of
England as
Norman round churches (e.g. the
Round Church in
Cambridge, near
Trinity College).
But the (Ethiopian) Copts were there before the Crusaders! And they had a church, which the crusaders "rebuilt" into their own structure. So the Copts got pushed up to the rooftop. Today there is still a small Coptic monastery on the roof of the Holy Sepulchre, built with very African-looking mud huts. They also have a small church inside the main structure, near the roof and their monastery.
It used to be that the Coptic monks would let you descend from their monastery to the main building, via their church. Nowadays there are just too many visitors, and I don't think they allow it to most people.
An Accord signed in Vienna towards the end of the 19th century fixed property rights of the imperial powers in Jerusalem. Part of the accord divided up the church between the factions. Every chapel, room, church, floor, wall or ceiling in the structure belongs to one of the churches! In one memorable case, a lightbulb burnt out, but couldn't be replaced since the ceiling (and hence the lightbulb) belonged to one church, while the floor (on which the ladder would have to rest) belonged to another. Eventually the commander of police in Jerusalem held protracted negotiations with the heads of the churches, while his deputy pushed in a ladder and replaced the bulb. (This should be probably be understood as having taken place with the tacit consent of all present; the end result was the replacement of the bulb, without any of the sides' rights being diluted).