In this paper, we study the Steiner 2-edge connected subgraph polytope.
We introduce a large class of valid inequalities for this polytope called
the generalized Steiner F-partition inequalities, that generalizes
the so-called Steiner F-partition inequalities. We show that these
inequalities together with the trivial and the Steiner cut
inequalities completely describe the polytope on a class of graphs
that generalizes the wheels. We also describe necessary conditions for
these inequalities to be facet defining, and as a consequence, we
obtain that the separation problem over the Steiner 2-edge connected
subgraph polytope for that class of graphs can be solved in polynomial
time. Moreover, we discuss that polytope in the graphs that decompose
by 3-edge cutsets. And we show that the generalized Steiner
F-partition inequalities together with the trivial and the Steiner
cut inequalities suffice to describe the polytope in a class of graphs
that generalizes the class of Halin graphs when the terminals have a
particular disposition. This generalizes a result of Barahona and
Mahjoub [4]
for Halin graphs. This also yields a
polynomial time cutting plane algorithm for the Steiner 2-edge
connected subgraph problem in that class of graphs.