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We show that not all $(2+1)$ dimensional toric phases are Seiberg-like duals.Particularly, we work out superconformal indices for the toric phases of Fanos${\cal{C}}_3$, ${\cal{C}}_5$ and ${\cal{B}}_2$. We find that the indices forthe two toric phases of Fano ${\cal{B}}_2$ do not match, which implies thatthey are not Seiberg-like duals. We also take the route of acting Seiberg-likeduality transformation on toric quiver Chern-Simons theories to obtain dualquivers. We study two examples and show that Seiberg-like dual quivers are notalways toric quivers.

Is toric duality a Seiberg-like duality in (2+1)-d ?