  The Thurston norm of a 3-manifold measures the complexity of surfaces
representing two-dimensional homology classes. We study the possible unit balls
of Thurston norms of 3-manifolds $M$ with $b_1(M) = 2$, and whose fundamental
groups admit presentations with two generators and one relator. We show that
even among this special class, there are 3-manifolds such that the unit ball of
the Thurston norm has arbitrarily many faces.
