1. The problem statement, all variables and given/known data 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. 2. Relevant equations 3. 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?