A multi-plane circuit structure has at least a first circuit plane and a second circuit plane, and each circuit plane has a plurality of row wire segments, a plurality of column wire segments, and a plurality of crosspoint devices formed at intersections of the row wire segments and the column wire segments. The row and column wire segments have a segment length for forming a preselected number of crosspoint devices thereon. Each row wire segment in the second circuit plane is connected to a row wire segment in the first circuit plane with no offset in a row direction and in a column direction, and each column wire segment in the second circuit plane is connected to a column wire segment in the first circuit plane with an offset length in both the row direction and the column direction. The offset length corresponds to half of the preselected number of crosspoint devices.