Arjun,
All rotations are around primary axes of the icosohedron -- NOT the x,y,z primary axes inherent to SketchUp. Rotations around non-primary axes is readily-available in SketchUp, but you have to dig, a bit, into the Users Guide. Here's a description:
The trick is to use the "click & drag" technique, to (re)define endpoints of the axis of rotation. I use the icosahedron center & a face-vertex to define 72° rotations. For 120° rotations, I use the center of the equilateral-triangle face of the icosahedron. (I generally place a guide-point at face centers, to be used as "inference" for subsequent rotations.)
I could not model geodesic domes/spheres without this rotation method. While it's not really a "trick," most users, who are new to SketchUp, do not know about, or do not employ, this critical rotation feature of the program.
Absolutely, an essential SketchUp technique....
-Taff