  We construct and study a two parameter gauged linear sigma model with gauge
group $(U(1)^2\times O(2))/{\mathbb Z}_2$ that has a dual model with gauge
group $(U(1)^2\times SO(4))/{\mathbb Z}_2$. The model has two geometric phases,
three hybrid phases and one phase whose character is unknown. One of the
geometric phases is strongly coupled and the other is weakly coupled, where
strong versus weak is exchanged under the duality. They correspond to two
Calabi-Yau manifolds with $(h^{1,1},h^{2,1})=(2,24)$ which are birationally
inequivalent but are expected to be derived equivalent. A region of the
discriminant locus in the space of Fayet-Iliopoulos-theta parameters supports a
mixed Coulomb-confining branch which is mapped to a mixed Coulomb-Higgs branch
in the dual model.
