Involved in the biosynthesis of isoprenoids. Catalyzes the 1,3-allylic rearrangement of the homoallylic substrate isopentenyl (IPP) to its allylic isomer, dimethylallyl diphosphate (DMAPP). isopentenyl diphosphate = dimethylallyl diphosphate kcat is 29.9 sec(-1) for isomerase activity with IPP (at pH 6 and 60 degrees Celsius). Homooctamer. Dimer of tetramers. Belongs to the IPP isomerase type 2 family.