  This work is dedicated to the results were got in the model theory of the
regular polygons. We give the characterization of the monoids with
axiomatizable and model complete class of regular polygons. We describe the
monoids with complete class of regular polygons which satisfy the additional
conditions. We study the monoids, whose regular core is presented as a union of
the finite number of principal right ideals, all regular polygons over which
have the stable and superstable theory. We prove the stability of the
axiomatizable model complete class of regular polygons and we also describe the
monoids with the superstable and $\omega$--stable class of regular polygons
when this class is axiomatizable and model complete.
