  The coframe field model is known as a viable model for gravity. The principle
problem is an interpretation of six additionaldegrees of freedom. We construct
a general family of connections which includes the connections of Levi-Civita
and Weitzenb\"{o}ck as the limiting cases. We show that for a special choice of
parameters, a subfamily of connections is invariant when the infinitesimal
field of transformations (antisymmetric tensor) satisfies the pair of vacuum
Maxwell equations -- one for torsion and one for non-metricity. Moreover, the
vacuum Maxwell equations turn to be the necessary and sufficient conditions for
invariance of the viable coframe action (alternative to GR). Consequently, for
the viable models, the coframe field is proved to have the Maxwell-type
behavior in addition to the known gravity sector.
