The dispersion relation for (light/sound) in uniform medium is ω = c|k| where c is the speed of (light/sound) in this medium. The dispersion relationship forms a cone in k-space. When (light/sound) moves through a crystal, it diffracts at the Brillouin zone boundaries. If the speed of (light/sound) does not vary greatly throughout the crystal, the dispersion relation will be nearly a cone except near the Brillouin zone boundaries where it will bend to strike the boundaries at 90°. The dispersion relation in a reduced zone scheme can be approximated by placing the apex of a cone at every reciprocal lattice point, ω = c|k - G|. The empty lattice approximation draws one band per Brillouin zone. For photons, there are two polarizations for every $k$-state. These polarizations may have different frequencies if the material is anisotropic. Phonons have one longitudinal and two transverse modes per $k$-state. Because of this, phonon dispersion curves will show two or three branches where the empty lattice approximation only has one.

Cross sections of this collection of cones are taken in the high symmetry directions of the Brillouin zone to produce the dispersion relation. The resulting (photonic/phononic) band structures for some crystals are plotted below in various high symmetry directions of k-space.

1-D
2-D square	2-D hexagonal
Simple cubic	Face centered cubic
Body centered cubic	Hexagonal
Tetragonal	Body Centered Tetragonal
Orthogonal