Gauge invariant discretization of Poincaré quantum gravity

In this Letter we suggest gauge invariant discretization of Poincaré quantum gravity. We generalize Regge calculus to the case of Riemann-Cartan space. The basic element of the constructed discretization is piecewise-linear Riemann-Cartan space with flat pieces of hypercubic form. We consider the model with squared curvature action and calculate the correspondent lattice action. We construct local measure over the dynamical variables of the lattice model.