Abstract: To construct the spherical patterns by the nonlinear planar iterating mappings,we present a way of constructing continuous-tiling chaotic attractors on the surface of the hexahedron in 3-space by the planar symmetry mappings based on the square lattice.The conditions on the square boundary,which the planar symmetry mappings should satisfy,to construct continuous-tiling chaotic attractors on the hexahedron were proposed.Three plane mappings were formed by the truncated Fourier series.The two plotting windows were found.Based on the boundary symmetric characteristic of the two plotting windows,the chaotic attractors in the plane or on the hexahedron can be continuously generated by the three mappings.Experiments show that the planar mappings based on the square lattice presented in this paper can be used to automatically construct a great number of the continuous-tiling chaotic attractors on the hexahedron in 3-space.