Measurements on powders or polycrystalline samples require evaluation and calculation functions and integrals over the whole domain, most often a Brillouin zone, of the dispersion relations of the system of interest. Sometimes the symmetry of the system is high, which causes the shape of the functions describing the dispersion relations of the system to appear many times over the whole domain of the dispersion relation. In such cases the effort to calculate the DOS can be reduced by a great amount when the calculation is limited to a reduced zone or fundamental domain. The Brillouin zone of the face-centered cubic lattice (FCC) in the figure on the right has the 48-fold symmetry of the point group O h with full octahedral symmetry. This configuration means that the integration over the whole domain of the Brillouin zone can be reduced to a 48-th part of the whole Brillouin zone. As a crystal structure periodic table shows, there are many elements with a FCC crystal structure, like diamond, silicon and platinum and their Brillouin zones and dispersion relations have this 48-fold symmetry. Two other familiar crystal structures are the body-centered cubic lattice (BCC) and hexagonal closed packed structures (HCP) with cubic and hexagonal lattices, respectively. The BCC structure has the 24-fold pyritohedral symmetry of the point group T h. The HCP structure has the 12-fold prismatic dihedral symmetry of the point group D 3h. A complete list of symmetry properties of a point group can be found in point group character tables.