# Group Actions on Truncated Octahedron

## Homework Statement

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?