I have been thinking about building a Dome house (or 2 or 3 smaller domes connected) for several years. Looked at basalt/concrete and then aircrete.
I went to an aircrete dome/arch building workshop a few weeks ago. We learnt how to make and build the structure. The bricks are light and easy to build with. They need to be coated with a mesh, say a fibreglass one along with a couple coats of render but still come out way cheaper than many other types of building, are fire resistant and termite resistant. The dome and or arch create strength by compression.
There are lots of sites to see designs and ways to make them. I have just engaged an architect and engineer who believe they can sign off that the building will meet Australian Standards, and that is in a bush fire special rural area (lots of legislation). Water harvesting from the curved roof seems to be a harder aspect but can be done. Let me know if you need links. Dome Gaia are just starting an online course with extended discount (24 hours), but maybe that has finished already.