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Though the lattice cells are not spherically symmetric, the dispersion relation still has spherical symmetry from the point of view of a fixed central point in a reciprocal lattice cell if the dispersion relation is extended outside the central Brillouin zone. The [[density of states#Parabolic dispersion|density of states]] in a three-dimensional lattice will be the same as in the case of the absence of a lattice. For the three-dimensional case the density of states <math>D_3\left(E\right)</math> is;
:<math>D_3\left(E\right) = 2 \pi \sqrt{\frac{E-
In three-dimensional space the Brillouin zone boundaries are planes. The dispersion relations show conics of the free-electron energy dispersion parabolas for all possible reciprocal lattice vectors. This results in a very complicated set intersecting of curves when the dispersion relations are calculated because there is a large number of possible angles between evaluation trajectories, first and higher order Brillouin zone boundaries and dispersion parabola intersection cones.
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