Diameter of the STOMACH graph.

How many moves does it take to go from the tiling on the left to the tiling at the right?

(The answer is 11.)

How many pairs of tilings require 11 moves to reach each other?

(Ans: 4. Which four pairs? )

Now try the following pair of tilings.
How many moves are required to go from one to the other?
This is the distance between them in the STOMACH graph.