There's a lot of good info on Stardomes and Geodesics (and also tipis and yurts too) at
http://www.simplydifferently.org/. The site owner's spent several years living full time in a range of these structures and really knows his stuff, including online calculators to work out the lengths of poles for you.
The HUGE advantage of stardomes over the geodesics is:
- 15 bendable struts (optional add 2 for the base), all the same length
- no connectors, no complicated calculations (e.g. to reduce waste)
- simple bow crossings, which can be tied with cords to provide stability
As you can see very different from a "traditional" geodesic.
The problem is though, the Japanese are making these from split bamboo, and we can't really get hold of this. Even if you can get hold of a large diameter bit of bamboo, you probably can't get the length, it'll be very expensive, and it'll have been dried and so a nightmare to split.
Of course, you could rake out your collection of spare aluminium dome tent poles, but then you may as well use a dome tent. I'm sure it could be made up with coppiced wood, using two or three bound together for each pole.
I'm also looking at using plywood. I reckon one 8'x4' sheets could potentially make a 15' (4.58 metre) diameter dome, which would be plenty big enough.
You'd need to cut the plywood into 1" wide strips, which would give you 45 + sawdust. They could be bound together, or bolted with an overlap, or some kind of collar fabricated even.
But that's as far as I've got without a trip to the timber merchants. I want to see what kind of thickness I'll need to balance strength, flexibility, and weight. I'm thinking something around 1/2 inch thick, but that's just off the top of my head.
And then cover with a tarp, or a parachute to start, make up a shaped cover if it looks like it'll work.