A method of co-extruding a central portion of a honeycomb body with an integral skin, the method comprising the steps of: providing a die body including an array of pins that are spaced apart to define an extrusion face with a honeycomb network of discharge slots extending along an extrusion axis of the die body, the die body further including an outer peripheral surface facing away from the extrusion axis and circumscribing the extrusion face, wherein the honeycomb network of discharge slots at least partially defines a first skin flow characteristic at a first location of the outer peripheral surface and at least partially defines a second skin flow characteristic at a second location of the outer peripheral surface spaced from the first location in a direction about the extrusion axis; providing a mask including an inner peripheral surface; and mounting the mask to the die body such that the inner peripheral surface at least partially circumscribes the outer peripheral surface of the die body to define a peripheral gap between the inner peripheral surface and the outer peripheral surface that circumscribes the array of pins, and wherein the peripheral gap includes a first extrusion cross section associated with the first location of the outer peripheral surface, and the peripheral gap includes a second extrusion cross section associated with the second location of the outer peripheral surface, wherein an overall flow area of the first extrusion cross section is arranged to be less than an overall flow area of the second extrusion cross section; configuring the first extrusion cross section and the second extrusion cross section to at least partially compensate for the difference between the first skin flow characteristic and the second skin flow characteristic, wherein the step of configuring includes configuring one of the inner peripheral surface and the outer peripheral surface such that the inner peripheral surface is not geometrically similar with the outer peripheral surface, and wherein the step of configuring provides one of the inner peripheral surface and the outer peripheral surface with a lobed frustoconical surface; extruding a quantity of batch material through an overall peripheral flow area of the peripheral gap while extruding another quantity of the batch material through the honeycomb network of discharge slots such that a central portion of the honeycomb body is co-extruded with an integral skin defining an outer periphery of the honeycomb body. providing a die body including an array of pins that are spaced apart to define an extrusion face with a honeycomb network of discharge slots extending along an extrusion axis of the die body, the die body further including an outer peripheral surface facing away from the extrusion axis and circumscribing the extrusion face, wherein the honeycomb network of discharge slots at least partially defines a first skin flow characteristic at a first location of the outer peripheral surface and at least partially defines a second skin flow characteristic at a second location of the outer peripheral surface spaced from the first location in a direction about the extrusion axis; providing a mask including an inner peripheral surface; and mounting the mask to the die body such that the inner peripheral surface at least partially circumscribes the outer peripheral surface of the die body to define a peripheral gap between the inner peripheral surface and the outer peripheral surface that circumscribes the array of pins, and wherein the peripheral gap includes a first extrusion cross section associated with the first location of the outer peripheral surface, and the peripheral gap includes a second extrusion cross section associated with the second location of the outer peripheral surface, wherein an overall flow area of the first extrusion cross section is arranged to be less than an overall flow area of the second extrusion cross section; configuring the first extrusion cross section and the second extrusion cross section to at least partially compensate for the difference between the first skin flow characteristic and the second skin flow characteristic, wherein the step of configuring includes configuring one of the inner peripheral surface and the outer peripheral surface such that the inner peripheral surface is not geometrically similar with the outer peripheral surface, and wherein the step of configuring provides one of the inner peripheral surface and the outer peripheral surface with a lobed frustoconical surface; extruding a quantity of batch material through an overall peripheral flow area of the peripheral gap while extruding another quantity of the batch material through the honeycomb network of discharge slots such that a central portion of the honeycomb body is co-extruded with an integral skin defining an outer periphery of the honeycomb body.