Abstract: A Bianchi group is a group of the form PSL2(O_k), where O_k is the ring of integers of an imaginary quadratic number field k. In this talk, after revisiting the classical case of PSL2(Z) acting on the upper half-space, I will give an introduction to Bianchi groups and their action on the hyperbolic 3-space. I will then present a computational approach to defining a deformation retract of the hyperbolic 3-space which is invariant under this action. We will also see some 3D pictures of how this deformation retract looks like. Finally, I will outline how one can obtain a presentation of the Bianchi group from the deformation retract.