  We produce a Schwarz lemma for the symmetrized tridisc \[ \mathbb G_3 =\{
(z_1+z_2+z_3,z_1z_2+z_2z_3+z_3z_1,z_1z_2z_3): \,|z_i|< 1, i=1,2,3 \}. \] We
show that an interpolating function related to the Schward lemma for $\mathbb
G_3$ is not unique and present an explicit description of all such
interpolating functions. We also study the complex geometry of $\mathbb G_3$
and present a variety of new characterizations for the open and closed
symmetrized tridisc.
