  Regge action is represented analogously to how the Palatini action for
general relativity (GR) as some functional of the metric and a general
connection as independent variables represents the Einstein-Hilbert action.
  The piecewise flat (or simplicial) spacetime of Regge calculus is equipped
with some world coordinates and some piecewise affine metric which is
completely defined by the set of edge lengths and the world coordinates of the
vertices. The conjugate variables are the general nondegenerate matrices on the
3-simplices which play a role of a general discrete connection. Our previous
result on some representation of the Regge calculus action in terms of the
local Euclidean (Minkowsky) frame vectors and orthogonal connection matrices as
independent variables is somewhat modified for the considered case of the
general linear group GL(4,R) of the connection matrices.
  As a result, we have some action invariant w. r. t. arbitrary change of
coordinates of the vertices (and related GL(4,R) transformations in the
4-simplices). Excluding GL(4,R) connection from this action via the equations
of motion we have exactly the Regge action for the considered spacetime.
