Abstract: The metallic crystal structures inspired edge-to-edge tessellations and a tessellation based lattice structures are disclosed. In accordance with an exemplary embodiment of the invention, basic unit lattice cells are stacked and connected to constitute a three-dimensional tessellations, wherein each of the basic unit lattice cells comprises a multiple flat connecting portions formed on a surface of the basic unit lattice cell and intersecting with a multiple of axes intersecting in a center of the basic unit lattice cell, and the flat connecting portions of one of the basic unit lattice cell is connected to the flat connecting portions of the adjacent basic unit lattice cell to constitute a connection structure of edge-to-edge tessellation. The formed tessellations are periodically tessellated in a design domain to form different tessellated lattice structures. The Functionally Tessellated (FT) lattice structures composed of different tessellations by interlocking into each other are also disclosed.