A lightweight periodic cellular structure has a stacked array of hollow or solid structural elements that are bonded at their contact points in order to form a stacked lattice structure. Further arrays may be stacked onto the stacked lattice structure in order to form a periodic cellular structure of varying thickness and depth. Also, structural panels may be added to parallel exterior edges of the stacked lattice structure to form a structural panel. Further, the hollow structural elements are provided with wicking elements along their interior walls to facilitate heat transfer through the periodic cellular structure. Liquid may also be introduced into the hollow structural elements to further facilitate heat transfer through the periodic cellular structure. Also, the cellular structure may be utilized as light weight current collectors, such as electrodes, anodes, and cathodes. The related method of manufacturing the periodic cellular structure can accommodate a variety of cross-sectional shapes, introduce a variety of stacking offset angles to vary the lattice shape and resultant mechanical characteristics of the periodic cellular structure; and allow for the bending of the array of hollow or solid structural elements into an array of hollow pyramidal truss elements that can be used to form a stacked pyramidal.