After practicing making the 5 platonic solids, using Michaels method of
twin, vertical, intersecting rotation circles, strategically centered, perpendicular to an objects axis of rotation,
and passing through the vertex to be joined, http://moi3d.com/forum/index.php?webtag=MOI&msg=2140.46
it was very easy to construct a geodesic dome. It was not necessary to use any dihedral angles.
Rotate axis and Array Circular were used multiple times.

The variety of geodesic dome was selected from here: http://simplydifferently.org/Geodesic_Dome_Notes?page=3
It is called the "3V 5/9 Icosahedron Dome." This dome is made up of 3 different lengths of materials, in the form of line
segments, which form two different isosceles triangles.

(I build one out of 2x4's and plywood, a number of years ago, long since rotted away...)

Or you can just import a model from somewhere...







The top "4/9ths" of the dome can be copy rotated about the top pentagonal vertex, and moved vertically downward,
to create the full "spherical" dome.