Before revision:  Using a method proposed in earlier work, we prove the existence of recognizable 2-dimensional morphisms \omega_i:i+1} \Omega_i for every i\in\{0, 1, 2 , 3,6,7,8,9,10,11\} that are onto up to a shift. Each \omega_i maps a tile on a tile or on a domino of two tiles . We also prove the existence of a topological conjugacy \eta:\Omega_6 \Omega_5 which shears Wang tilings by the action of the matrix and an embedding \pi:\Omega_5 \Omega_4 that is unfortunately not onto.
After revision:  Using a method proposed in earlier work, we prove the existence of recognizable 2-dimensional morphisms \omega_i:i+1} \Omega_i for every i\in\{0, 1, 2 ,  \Omega_5 which shears Wang tilings by the action of the matrix and an embedding \pi:\Omega_5 \Omega_4 that is unfortunately not onto.