A hierarchical sandwich core in the form of a honeycomb, i.e. having repetitive and periodic lattice materials. The sandwich core can be made up of a macroscopic honeycomb structure with sandwich cell walls having a mesoscopic cellular core. The longitudinal axis of cells of the mesoscopic honeycomb cell can be perpendicular to the longitudinal axis of the cells of the macroscopic honeycomb structure. Alternatively, if a foam core is used having mesoscopic cells the shape of the mesoscopic cells can be made during the foaming process so that they are elongate in a direction perpendicular to the longitudinal axis of the cells of the macroscopic honeycomb structure.