I have done several. I take it there are no sales of similar domes around? You have to figure out how the market will react to them in your area. I was normally lucky enough to find one to a few dome sales. I often found, in the market I was appraising in, that they had market reactions similar to round (octagon) homes.
I'm assuming a dome home is similar to an octagon home, isn't it?
You have to remember your math to figure out square footage, that took me a while, then I explained and explained the subject property, the neighborhood, and the market. The market I was working in had no 'dome' homes so I used the odd sales of similar size and explained and explained some more. Probably had three or four pages of comments.
You might have to go back in time 2-4 years or outside your normal area that you would search for comps. Supposedly, they are very energy efficient.
To calculate square footage, measure each section and at the base of each section, measure from the corners to the geometric center of the building. If it is 8 sided, then you will have 8 triangles. Calculate the SF of 1 triangle and multiply by the number of sections. If there is an upstairs, it will be more difficult as you cannot always measure the base and the interior walls might conceal where the base starts and stops. BUT, measure from an outside wall to the geometric center. Calculate it as if were a semi circle.
If you can work from a set of plans, you will be more accurate.
Here in SE Cheeseland they're scattered around and you can usually find a comp or two even if they're old. I appraised one about two years ago for bankruptcy purposes and had three sales within a year and half. The homeowner was happier than hell because he was hoping it would be worth far less than the assessment and the data showed it was worth far less than the assessment. I've probably appraised ten of them through the years, and they always smell musty because of humidity problems. Here they are mostly circles, and I give 'em the old Pi R Squared. For the second floor I subtract the open Pi R squared from the middle.
Here's a pic of a dome home duplex I ran across as a listing while appraising a duplex out in the country. If, and that's a big if, this thing ever sells and comes through my office, I very well may be on vacation. At least until it closes.