DNA is a useful material for nanoscale construction. Due to highly specific Watson-Crick base pairing, the DNA sequences can be designed to form small tiles or origami. Adjacent helices in such nanostructures are connected via Holliday junction-like crossovers. DNA tiles can have sticky ends which can then be programmed to form large one-dimensional and two-dimensional periodic lattices. Recently, a three-dimensional DNA lattice has also been constructed. Here we report the design and construction of a novel DNA cross tile, called the double-decker tile. Its arms are symmetric and have four double helices each. Using its sticky ends, large two-dimensional square lattices have been constructed which are on the order of tens of micrometers. Furthermore, it is proposed that the sticky ends of the double-decker tile can be programmed to form a three-dimensional periodic lattice with large cavities that could be used as a scaffold for precise positioning of molecules in space.