Delzant type theorem for torus-equivariantly embedded toric hypersurfaces

In the previous work, we study the moment polytope of the closure of the complex subtorus orbit in a symplectic toric manifold associated to an affine subspace when the closure is a smooth complex submanifold. In this paper, we clarify the condition for nonsingularity of the closure of the codimension one complex subtorus orbit in terms of polytopes. The main result is a generalization of Delzant theorem.