How to find the number of ways in which six digits 1,2,..,6 can be assigned to six faces of a cube (without repeatation 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 12x2=24.
Am I correct? Please suggest better approach approach or bijections(if there are any).