Each face of a fair cubical die is labelled with one of the numbers through . On every face an arrow is drawn pointing to one of its four neighbouring faces. Suppose these arrows have the property that, beginning at any face and repeatedly moving to the face its arrow indicates, the six moves visit all six faces before returning to the face where you began. In how many different ways can the arrows be drawn so that this property holds?
A
B
C
D
E
F
G
H