Theory
b₁ = 2π(a₂×ẑ)/(a₁·a₂×ẑ)
b₂ = 2π(ẑ×a₁)/(a₁·a₂×ẑ)
a_i · b_j = 2π δᵢⱼ
The Brillouin zone is the Wigner-Seitz cell of the reciprocal lattice — the set of k-points closer to the origin than to any other reciprocal lattice point. It encodes all distinct crystal momenta.