For any graded poset $P$, we define a new graded poset, $mathcal E(P)$, whose elements are the edges in the Hasse diagram of P. For any group, $G$, acting on the boolean algebra, $B_n$, we conjecture that $mathcal E(B_n/G)$ is Peck. We prove that the
conjecture holds for common cover transitive actions. We give some infinite families of common cover transitive actions and show that the common cover transitive actions are closed under direct and semidirect products.
