  The partition function corresponding to the "polytopic" action, a new action
for the gravitational interaction which we have proposed recently, is computed
in the simplest two-dimensional geometries of genus zero and one. The
functional integral over the Liouville field is approximated by an ordinary
integral over the constant zero mode. We study the dependence on both the
coupling constant and the cosmological constant, and compare with recent
scaling results in standard 2D quantum gravity.
