  A discrete theory of gravity locally invariant under the Poincar\'e group is
considered as in a companion paper. We define a first order theory, in the
sense of Palatini, on the metric-dual Voronoi complex of a simplicial complex.
We follow the same spirit of the continuum theory of General Relativity in the
Cartan formalism. The field equations are carefully derived taking in account
the constraints of the theory. They look very similar to first order Einstein
equations in the Cartan formalism. It is shown that in the limit of {\it small
deficit angles} these equations have Regge Calculus, locally, as the only
solution. A quantum measure is easly defined which does not suffer the
ambiguities of Regge Calculus, and a coupling with fermionic matter is easily
introduced
