Metal roof over pitch-wise sleepers. With a continuous ridge vent and eave vents. The 'hot tin roof' drives a passive ventilation system AKA free air-conditioning.
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I have many concerns about domes. The first being of noise isolation between rooms. I want a place where loud movies could be played while others sleep. I also don't like how much roofing material is used, and the difficulty in replacing it due to the compound shape.... Beyond that, I don't know what the advantages are.
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I've only lived in one dome myself; but TLDR it was the cleanest quietest and warmest place I've ever lived [Alert:small sample size].
Cleanest because, if you think about it dust settles in corners. When the air circulates in a torus shape inside a[n approximate] hemipshere, the dust leaves with the ventilation air.
Quietest because outside sounds can't get in! And if the speakers are placed appropriately, they don't need as much power to reach whatever level you desire. And the neighbors won't complain. OTOH, with a saddle-curved entry tunnel the whole structure becomes a instrument in the landscape. Don't point it at the neighbors house.
Warmest because it had radiant floor heat in the concrete slab. The biggest problem was in the winter you had to wear slippers. It was cheap-@ss construction T-111 siding asphalt shingles,
aluminum window frames. A well constructed dome might be low-heat-loss and be heated by a copper globe full of (solar heated) water in the skylight. (the weight would act as a keystone, post-stressing the whole thing)
Oh—noise: All walls are radial to the center; no hallways, just alcoves. In an open dome sound travels along the surface; you can face the wall and whisper and someone on the other side can hear, but someone in the middle can not. Contrarywise, all the sound that passes through the middle can be muffled by a cylindrical absorber (maybe a spiral staircase). Or, cancelled with a speaker....
I'd better stop. Why isn't this in Saving@Home?