1. The problem statement, all variables and given/known data How many ways can you color the edges of a hexagon in two colors? It is assumed two colorings are identical if there is a way to flip or rotate the hexagon. 2. Relevant equations Orbit Stabilizer Lemma and Burnside's Lemma 3. The attempt at a solution This, implements the Orbit Stabilizer Lemma and Burnside's Lemma (think necklace permutations) however, is there anything special or different to computing this because you are now dealing with the faces/edges rather than the vertices (or beads of a necklace)? Thanks.