How to find the number of ways in which six digits $1,2,..,6$ can be assigned to six faces of a cube (without repetition of digits) so that one arrangement cannot be obtained from another by a rotation of the cube?
I tried to find the number of unique $4-$adjacencies of the faces of the cube. I drew a simple undirected graph $A,B,...,F$ having $6$ vertices with each of them having degrees equal to $4$. There were $12$ edges. Considering the choice between the top and the bottom of the cube, I found the result to be $12 \times 2=24.$
Am I correct? Please suggest better approach approach or bijections(if there are any).