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By treating the cosmological constant as a thermodynamic pressure, weinvestigate the thermodynamic behaviors of Born-Infeld AdS black hole in 4DEinstein-Gauss-Bonnet (EGB) gravity. The result shows that the Van der Waalslike small/large black hole (SBH/LBH) phase transition always appears for anypositive parameters $\alpha$ and $\beta$. Moreover, we observe a new phenomenonof small/intermediate/large black hole (SBH/IBH/LBH) phase transition with onetricritical and two critical points in the available parameter region for\alpha and \beta. This behavior is reminiscent of the solid/liquid/gas phasetransition.

Triple points and phase diagrams of Born-Infeld AdS black holes in 4D Einstein-Gauss-Bonnet gravity