Abstract: The present disclosure is directed to a novel honeycomb substrate, an extrusion die apparatus for forming the novel substrate, as well as a method for extruding the honeycomb structure. This inventive honeycomb structure possesses a matrix of straight cell walls defining a plurality of straight flow cells running generally parallel to the axis of extrusion, as well as a matrix of cross-directional or corrugated cell walls defining a plurality of flow channels some of which may be at an angle, preferably perpendicular to the axis of extrusion or to the straight flow channels. The extrusion die apparatus is generally comprised of primary and secondary feed holes and associated discharge slots and, preferably a device for causing buckling of the extrudate which exits the primary slots.