In language of loop quantum gravity, 4d and 3d space-time can be constructed by 4d  and 3d spinfoam models respectively. We consider a Kaluza-Klein like approach for a 4d spin foam model. We apply this approach to a 4d TOCY model based on group field theory; and using the Peter-Weyl expansion of the gravitational field then we reconstruct at once a 3d simplicial complex representing spacetime and its geometry; like in the Ponzano-Regge formulation of pure 3d quantum gravity plus the Feynman graph for matter like fields. Thus We find a mechanism for generation of matter and new dimensions from pure gravity.