This is super fascinating! You mention snow, but I didn't notice what part of the world you're living in. I'd be curious about building something like this, but I'm in a part of Canada where -40 and LOTS of snow is a real possibility.
If you have lots of snow, then I would advise a sparse frame , imagine an outline of octagons and pentagons but not the internal triangles, more insulation would also be required.
I live in the mountains of North Carolina: A temperate but very wet area.