how to support a spherical dome?
The wooden Dome of the rock Rotskoepel (end 7th century - Jeruzalem) with a perimeter of 20,44 m seems to be supported by an octogonal building, but it isn't. In rality it is supported by a ring of colums. The octogon is just built around it.
How to support a spherical dome?
The most logical support of a spherical dome is a cylinder. But a cylinder has, apart of the use as independant building little constructive possibilities. In Classical Antiquity round buildings are used as temples and aphitheatres.
If you want to use spherical domes in rectangular buildings, you'll have to think of solutions to support the round form of a spherical dome.