  We consider the Faddeev formulation of general relativity (GR), which can be
characterized by a kind of $d$-dimensional tetrad (typically $d$=10) and a
non-Riemannian connection. This theory is invariant w. r. t. the global, but
not local, rotations in the $d$-dimensional space. There can be configurations
with a smooth or flat metric, but with the tetrad that changes abruptly at
small distances, a kind of "antiferromagnetic" structure.
  Previously, we discussed a first order representation for the Faddeev
gravity, which uses the orthogonal connection in the $d$-dimensional space as
an independent variable. Using the discrete form of this formulation, we
considered the spectrum of (elementary) area. This spectrum turns out to be
physically reasonable just on a classical background with large connection like
rotations by $\pi$, that is, with such an "antiferromagnetic" structure.
  In the discrete first order Faddeev gravity, we consider such a structure
with periodic cells and large connection and strongly changing tetrad field
inside the cell. We show that this system in the continuum limit reduces to a
generalization of the Faddeev system. The action is a sum of related actions of
the Faddeev type and is still reduced to the GR action.
