1. The problem statement, all variables and given/known data Not a homework question, but I am attempting to understand what exactly the first Brillouin zone is. 2. Relevant equations 3. The attempt at a solution From my textbook, what I'm gathering is that one constructs the first Brillouin zone by constructing a "Wigner-Seitz" type cell in reciprocal space. My question is, is this how one constructs the first Brillouin zone, and if so, why/how does this work?