On the basis of [7], we have the necessary theory to study the Heisenberg's group geometry. This paper goal is to carry the whole results to the tridimensional case. We are helped by the characteristics of the Ado theorema(see [3]): "All Lie algebra of dimension n can be characterized within the square matrix algebra of nxn".

On the basis of [7], we have the necessary theory to study the Heisenberg's group geometry. This paper goal is to carry the whole results to the tridimensional case. We are helped by the characteristics of the Ado theorema(see [3]): "All Lie algebra of dimension n can be characterized within the square matrix algebra of nxn".