Abstract: Aimed at the description concerning the first Brillouin zone of the face-centered cubic lattice and

body-centered cubic lattice in different textbooks，this paper provides intuitively the method of determining the first

Brillouin zone of these two structures by means of symmetric drawing. And through comparing the characteristics of

the five regular polyhedra that may exist in space，it puts forward a more rational and unified naming method for the

first Brillouin zone of these two kinds of lattice.

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