Let G be the group of rotational symmetries of the octahedron and consider the action of G on the edges of the truncated octahedron.
Describe the orbits of this action.
Choose one representative element in each orbit. Describe the stabilizers of these representative elements.
The Attempt at a Solution
I am having a lot of trouble visualizing the movements of the edges of the truncated octahedron (which is what I am assuming is what happens when G acts on them). But I think the edges of the square faces make up one orbit and I'm not sure on the others. Any thoughts?
Also, I don't really know what it means to pick a representative element of an orbit. Just pick one edge and see what the stabilizers are?