The design of the geodesic dome is a complicated matter. In part, this is because there is no one standard design. Rather, there are a number of designs based on taking a Platonic solid, such as an icosahedron, and then projecting each face onto the interior surface of the sphere. There is no perfect way to do this, as neither the angles nor the sides can be preserved without one distorting the other. The result of the design compromise is a regular pattern of triangles with their vertices lying approximately on the surface of the sphere. The edges of the triangles create "geodesics," great circles of a sphere, to distribute stress across the sphere. 

Geodesic designs can be extended to any curved, enclosed space, although, very oddly-shaped designs would require that each strut be individually calculated and fabricated, something which could render the structure especially expensive and complicated to construct. Because of the expense and complexity of design and fabrication of any geodesic dome, builders have tended to standardize on a few basic designs. [Citation: http://en.wikipedia.org/wiki/Geodesic_dome]