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Tesler polytope with hook sums a ∈ R n ≥0 is unimodularly equivalant to the flow polytopes on a complete graph of the net flow a. Morales conjectured that the Tesler polytope of hook sums all 1’s denoted by Tesn(1, . . . , 1) and the CRY polytope Tesn(1, 0, . . . , 0) are Ehrhart positive. We will first discuss how to approach the conjecture with Berline-Vergne’s construction of function α (BV-α) which satisfies the McMullen’s formula: |P ∩ Z n | = X F : face of P α(P, F) nVol(F), where nVol(F) is the normalized volume of F and α(P, F) only depends on the nomal cone of P at F. Since α only depends on normal cones and the normal cones are invariant under dilations, we obtain that (1.1) ei(P) = X F : i-dimensional face of P α(P, F) nVol(F), for any 1 ≤ i ≤ dim(P), where ei(P) is the i-th Ehrhart coefficient of P. One sees that, as a consequence of the above formula, if α(P, F) > 0 for every i-dimensional face of P, then ei(P) is positive. Moreover, if α(P, F) > 0 for every face of P, then P is Ehrhart positive. We say a polytope P is α-positive if α(P, F) > 0 for every face F of P. One benefit of using BV-α is the Reduction Theorem which implies that whenever a polytope P is α-positive then the same is true for any deformation Q of P. Therefore, it is natural to think about the deformations of Tesn(1, . . . , 1). We will see that any deformations of Tesn(1, . . . , 1) is a translation of some Tesler polytopes and use this fact to characterize which Flow polytopes on a complete graph are the deformations of Tesn(1, . . . , 1).