  A Schwarzschild type solution in Regge calculus is considered. Earlier, we
considered a mechanism of loose fixing of edge lengths due to the functional
integral measure arising from integration over connection in the functional
integral for the connection representation of the Regge action. The length
scale depends on a free dimensionless parameter that determines the final
functional measure. For this parameter and the length scale large in Planck
units, the resulting effective action is close to the Regge action.
  Earlier, we considered the Regge action in terms of affine connection
matrices as functions of the metric inside the 4-simplices and found that it is
a difference form of the Hilbert-Einstein action in the leading order over
metric variations between the 4-simplices.
  Now we take the (continuum) Schwarzschild problem in the form where spherical
symmetry is not set a priori and arises just in the solution, take the
difference form of the corresponding equations and get the metric (in fact, in
the Lemaitre or Painlev\'{e}-Gullstrand like frame), which is nonsingular at
the origin, just as the Newtonian gravitational potential, obeying the
difference Poisson equation with a point source, is cut off at the elementary
length and is finite at the source.
