  The paper continues the author's research in the problem of quantitative
investigation of basic curvelinear quasiinvariants of quasiconformal curves. It
concerns polygons with infinite number of vertices and provides various
distortion estimates in terms of intrinsic geometric characteristics of
polygons.
  In particular, this implies the coarse upper and lower estimates for the
Grunsky and Teichmuller norms of a conformal map of the disk onto any piecewise
$C^{1+}$-smooth bounded quasicircle.
