Random initial condition

Rules: hitting a corner flips corner, center and adjoint edges, hitting a edge flips edge and adjoint corners, hitting the center flips center and edges. The game plays in the abelian group (Z 2 ) 9 which is generated by the 9 involutions. Prove that you indeed can get any configuration by playing around.
For an introduction into the mathematical theory of finitely presented groups, see the book of G. Baumslag.

©, 1999