I'm just not sure exactly what these problems are asking me to do.
The first is
"Describe the decomposition of S into G-orbits." for a set S and a group G acting on S.
The second is
"Describe the orbits of poles for the group of rotations of a (insert platonic solid here)."
I think the first is asking for the cosets of the orbits in S.
The second asking for the generator formulas to give all elements of the given orbit.
I'm really not sure though as I can't seem to find reference to them in my text or notes.