An artificial honeycomb structure, and simple constructions therefrom, are provided, wherein at least a portion of at least one of the enclosing honeycomb cell walls is substantially porous, open, or permeable, and wherein at least one of the hollow cells comprises at least one substantially nonporous enclosing wall. The honeycomb and its constructions can be useful in applications that include, but are not limited to, heat exchange and storage, structural support, impact absorption, filtration, acoustic dampening, catalysis, and flow control and distribution.