Make a skeletal cube.
How many ways are there from one vertex, S to another, F?
Experiment with different ways of recording the journeys made.
Thread cotton from each vertex to opposite midpoints.
Try to anticipate what will happen as more and more threads are attached.
Finally what do you get?
Attach rods to vertices that are opposite.
What will happen when the cube is spun?
Spin between the fingers and see - were you right?