Catalysis of the reaction: (E)-4-hydroxy-3-methylbut-2-en-1-yl diphosphate + H2O + 2 oxidized ferredoxin = 2-C-methyl-D-erythritol 2,4-cyclodiphosphate + 2 reduced ferredoxin.
1-hydroxy-2-methyl-2-butenyl 4-diphosphate synthase activity