A honeycomb body having a repeating channel structure formed of intersecting porous walls. The repeating channel structure comprises a first channel type defined by at least four first surfaces, at least two of the at least four first surfaces are parallel to one another; and a second channel type having at least four second surfaces, wherein four or more of the at least four second surfaces are non-parallel with one another. Repeating channel structure is repeated in the honeycomb body. Honeycomb extrusion dies and methods of manufacturing the honeycomb body are provided, as are other embodiments.