(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.
Re:Japanese Dome House
by stan_rogers on Monday November 22, 2021 @02:40AM
(#29303839)
Geodesics usually have flat panels as well - flat panels of limited size meeting at odd angles, yes, but flat panels nonetheless - that allow you to use conventional furnishings against or nearby to walls without unusual visual gaps in at least a few places. "Real" domes, on the other hand, not so much.
The only way a half sphere works out well is if your dealing with some form of pressure dome. Either using internal pressure to support weight, or in the case of a building underwater/Moon/Mars dealing with very high pressure differences.