  The Jacobian algebra associated to a triangulation of a closed surface $S$
with a collection of marked points $M$ is (weakly) symmetric and tame. We show
that for these algebras the Auslander-Reiten translate acts 2-periodical on
objects. Moreover, we show that excluding only the case of a sphere with $4$
(or less) punctures, these algebras are of exponential growth. These four
properties implies that there is a new family of algebras symmetric, tame and
with periodic module category.
  As a consequence of the 2-periodical actions of the Auslander-Reiten
translate on objects, we have that the Auslander-Reiten quiver of the
generalized cluster category $\cC_{(S,M)}$ consists only of stable tubes of
rank $1$ or $2$.
