Two interlinked squares.

Two interlinked squares. You can think of this as two adjacent sides of a Rubic cube, flattened to lie on a plane. The left square and the right square have two vertices in common, v3 and v4. They share a single edge, e10. The edge numbers begin with 7 so that the group can be viewed as a subgroup of all permutations on 13 objects. Define a   Clockwise rotation through π/2 of the left square. b   Clockwise rotation through π/2 of the right square. A   Counter-clockwise rotation through π/2 of the left square. B   Counter-clockwise rotation through π/2 of the right square. a and b generate a subgroup of permutations on 13 objects. One can focus on the vertices alone, in which case a and b generate a subgroup of permutations on 6 objects. Similarly, a and b generate a subgroup of permutations on 7 objects, the edges. The four "radio buttons" below generate a, A, b & B. a   A   b   B   List of actions:   abAB     baBA     ABab     BAba