  After observing that the well-known convexity theorems of symplectic geometry
also hold for compact contact manifolds with an effective action of a torus
whose Reeb vector field corresponds to an element of the Lie algebra of the
torus, we use this fact together with a recent symplectic orbifold version of
Delzant's theorem due to Lerman and Tolman [LT] to show that every such compact
toric contact manifold can be obtained by a contact reduction from an odd
dimensional sphere.
