  We study the Faddeev formulation of gravity in which the metric is composed
of vector fields. This system is reducible with the help of the equations of
motion to the general relativity. The Faddeev action is evaluated for the
piecewise flat ansatz for these fields when the metric corresponds to the flat
interior of the 4-simplices of the general simplicial complex. Thereby an
analogue of the Regge action in the usual general relativity is obtained. A
peculiar feature of the Faddeev gravity is finiteness of the action on the
discontinuous fields, and this means possibility of the complete independence
of the fields in the different 4-simplices or incoincidence of the 4-simplices
on their common faces. The earlier introduced analogue of the Barbero-Immirzi
parameter for the Faddeev gravity is taken into account. There is some freedom
in defining the Faddeev action on the piecewise flat manifold, and the task is
set to make use of this freedom to ensure that this discrete system be
reducible with the help of the {\it discrete} equations of motion to the
analogous discrete general relativity (Regge calculus).
