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We study Faddeev formulation of gravity, in which the metric is composed ofvector fields. We consider these fields constant in the interior of the4-simplices of a simplicial complex. The action depends not only on the valuesof the fields in the interior of the 4-simplices but on the details of(regularized) jump of the fields between the 4-simplices. Though, when thefields vary arbitrarily slowly from the 4-simplex to 4-simplex, the latterdependence is negligible (of the next-to-leading order of magnitude).  We put the earlier proposed in our work first order (connection)representation of the Faddeev action into the discrete form. We show that uponexcluding the connections it is consistent with the above Faddeev action on thepiecewise constant fields in the leading order of magnitude. Thus, using thediscrete form of the connection representation of the Faddeev action can servea way to fix the value of this action on the piecewise constant ansatz onsimplices.

Faddeev formulation of gravity in discrete form