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We introduce the class of toric (2n, k)-manifolds, which are special class of closed, smooth manifolds M2n equipped with a smooth effective action of the compact torus Tk, 1 ≤ k ≤n and an open Tk-equivariant map μ : M2n →( R)k whose image is a convex polytope, where (R)k is considered with the trivial Tk-action.