Abstract: The solution of the volume of reduced Brillouin zone (BZ) is an important knowledge point in solid state physics. At present, the solution methods of BZ volume are generally different because of different BZ forms, which increases the teaching difficulty. In this paper, the reduced BZ is discretized into multiple pyramid with the origin of wave vector space as the common vertex, so that the solution of BZ volume is transformed into the sum of each pyramid. Taking the BZ volume solution of face-centered and body-centered cubic lattice as an example, it is obtained that the reduced BZ volume is the same as that of the reciprocal lattice primitive cell. The results show that the method is simple, intuitive and universal.

Key words: solid state physics, Brillouin zone, face-centered cubic lattice, body-centered cubic lattice