Abstract： There is a corresponding relation between a mapping point (D lattice point) in the RT (regular tetrahedron) and a DNA sequence (Zhang, 1991). A set of the D lattice points constructs a lattice (D lattice). The D lattice is proved to be a face-centered cubic lattice. The space distribution law of D lattice point is revealed.Based on the results the properties of Z curve (a intuitive tool for visualizing and analyzing the DNA sequence proposed by Zhang & Zhang) can be obtained naturally.Z curve bundle has symmetry of S4 group. Z curves constrain themselves within the inscribed sphere of the biggest regular tetrahedron etc.