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In this paper, for dimensionally continued gravity coupled to Born–Infeld electromagnetic field, we construct topological black holes in diverse dimensions and construct dyonic black holes in general even dimensions. We study thermodynamics of the black holes and obtain first laws. We study thermal phase transitions of the black holes in T–S plane and find van der Waals-like phase transitions for even-dimensional spherical black holes, such phase transitions are not found for other types of black holes constructed in this paper.