In mathematics, a Delzant polytope is a convex polytope in \mathbb{R}^n such for each vertex v, exactly n edges meet at v, and these edges form a collection of vectors that form a \mathbb{Z}-basis of \mathbb{Z}^n. Delzant's theorem, introduced by , classifies effective Hamiltonian torus actions on compact connected symplectic manifolds by the image of the associated moment map, which is a Delzant polytope.
