(Geodesic) domes are not usually half spheres at all. They can be but they really don't have to be. You can do more than half a sphere, half a sphere, less than half a sphere and all of them would be called domes.

https://en.wikipedia.org/wiki/Geodesic_dome

Some good sample images there.

And a geodesic dome does not require any internal supports, so it doesn't matter whether a pressure differential is involved.

Essentially any slice of a sphere can be made into a geodesic dome.