  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.
