The present disclosure relates to an electrical energy storage apparatus which forms an interpenetrating, three dimensional structure. The structure may have a first non-planar channel filled with an anode material to form an anode, and a second non-planar channel adjacent the first non-planar channel filled with a cathode material to form a cathode. A third non-planar channel may be formed adjacent the first and second non-planar channels and filled with an electrolyte. The first, second and third channels are formed so as to be interpenetrating and form a spatially dense, three dimensional structure. A first current collector is in communication with the first non-planar channel and forms a first electrode, while a second current collector is in communication with the second non-planar channel and forms a second electrode. A separator layers separates the current collectors.