Common 3D Lattices and Lattice Unit Cells

Simple Cubic Lattice -

which has lattice points on the corners of a cube, and the 3-D lattice is formed by translating the cube through space, using the orthogonal vectors ~a,~b and ~c, where |~a| = |~b| = |~c | There is one complete lattice point in the cube unit cell. (This is a Lattice Primitive Unit Cell.)

Figure 1.4 shows the a unit cell from of the simple cubic lattice.

Body Centered Lattice -

which has lattice points on the corners of a cube, and one in the center, and the 3-D lattice is formed by translating the cube through space, using the orthogonal vectors ~a,~b and ~c. There are two complete lattice points in the body centered cubic unit cell. (This is not a primitive
unit cell for the body centered lattice.)

Figure 1.5 shows the a unit cell from of the body centered cubic lattice.

Face Centered Lattice -

which has lattice points on the corners of a cube, and one each of the six faces, and the 3-D lattice is formed by translating the cube through space, using the orthogonal vectors ~a,~b and ~c. There are four complete lattice points in the face centered cubic unit cell. (This is not
a primitive unit cell for the face centered lattice.)

Figure 1.6 shows the unit cell of the face centered cubic lattice.