One of the first things we had to decide. There are two major types of dome homes that are build today: Geodesic Domes and Monolithic Domes.
A Geodesic Dome is based on the concepts popularized by R. Buckminster Fuller back in the 1940's. The basic idea is to take a sphere and approximate it with a series of triangular faces. This is normally done by actually starting with an icosahedron (think a 20 sided die) and then subdividing the edges and projecting the out on the circumscribed sphere. These are somewhat easy to construct, but being exact is difficult due to the number of triangular faces required for a smooth dome. If you are not very good then your dome will leak, causing both water damage problems and decreasing on the energy efficiency inherent in the dome shape.
About 30 years later David South designed the first Monolithic Dome. Monolithic means one stone, and the dome is exactly that. It is a dome shaped piece of concrete. How you build that is the trick. The process, in short, is to make it sort of like you make papier mache balloons. You blow up a really big balloon (well, a half balloon actually) and the cover it with concrete. In practice, you will cover the inside of the balloon (called an air form) with a layer of insulation and then spray concrete inside of that. The result is a structure that is very energy efficient (the walls are rated at at least R60 insulation and is very durable. Structurally they can withstand an F5 tornado or a category 5 hurricane. I actually had these structures pointed out to me by a fellow co-worker many years ago, Hank Wigley. Hank died in a car accident many years ago, but I still remember him.
Anyway, we have firmly decided on the Monolithic Dome concept and have made two trips to the factory in Italy, Texas to discuss the concept with them.