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The deformed Hermitian-Yang-Mills (dHYM) equation is a geometric PDE arising from Mirror Symmetry. In this talk we discuss the Kähler geometry of toric fibrations over complete flag manifolds, and exploit the large amount of symmetry here to convert the dHYM equation into a PDE on a convex polytope in Rⁿ. We will finish the talk with a specific example of toric variety, namely the blowup of projective space at a point, which will allow us to convert the PDE into an ODE, and hence allow us to determine algebraic conditions for the existence of solutions.