Lattices are structures formed of arrays of uniformly sized cells. Ceramic lattice nanostructures have been formed using hollow tubes of titanium nitride (TiN). Using vertex-connected, tessellated octahedra with 7-nm hollow struts with elliptical cross-sections and wall thickness of 75-nm produced approximately cubic cells 100-nm on a side at a scale of up to 1 cubic millimeter. The material's relative density was of the order of 0.013 (similar to aerogels).