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The dome will be an open skeletal structure. Probably with anchor points to hoist up a cover of sorts in the rain. Never thought of the acoustics inside a closed geodesic dome. I can easily see how it could be a nightmare! Frankly, I think geodesic dome houses are ugly. Here's a concept sketch. Dome might look like this. Or might not.
There is a guy named Gregg Fleishman who is building FASCINATING furniture and structures that use no nails - just slotted pieces of wood that fit together perfectly - and his structures are a fascinating look at some math I really don't understand. Some great ideas here: http://www.greggfleishman.com/structures.html Plus, his video on the "Lost Triangle of Pythagoras" plays nicely into your math camp: