The document discusses constructing a face-centered cubic (FCC) lattice and its reciprocal lattice in Mathematica. It defines the FCC lattice using basis vectors and plots the points. It then finds the basis vectors of the reciprocal lattice by solving equations. The reciprocal lattice is constructed and plotted similarly. High symmetry points and directions in the reciprocal lattice are identified. Finally, the dispersion relation along the [100] direction of the FCC lattice is plotted.