This work describes granular crystals held together by unusual, multipolar interactions and, under the application of an external bias, undergoing reversible structural transitions between closed and open forms. The system comprises two types of polymeric beads agitated on one or between two conductive plates and gradually acquiring charges by contact electrification. The charges thus developed induce a series of electrostatic images in the conductive supports and, in effect, the beads interact via dipolar or multipolar interactions, enabling the stabilization of non-electroneutral crystals. Furthermore, under an applied bias, the beads become polarized and their complex interactions (due to the series of image charges as well as series of image dipoles) result in open-pore crystals which return to compact forms upon bias removal. These effects are rationalized by analytical calculations, and the crystal structures observed in the experiments are reproduced by molecular dynamics simulations.