AgI nanoplates with unusual 7H and 9R polytype phases (see Figure) have been prepared in large quantities by a solution-based method using polyelectrolytes. The nanoplates exhibit extremely high conductivity, which is enhanced by four orders of magnitude compared to the macroscopic AgI phase (beta-AgI), and a surprising conductivity isotropy, both of which can be explained by mesoscopic ionic-conductivity effects in polytype heterostructures.