= Solution
A <Wigner-Seitz cell> is the region of real space at least as close to a chosen <Bravais lattice> point as to any other. It is bounded by perpendicular bisectors of vectors to neighboring lattice points and is a <primitive unit cell>.
A <reciprocal lattice vector> $\mathbf G$ satisfies $e^{i\mathbf G\cdot\mathbf R}=1$ for every <lattice translation> $\mathbf R$. With primitive vectors $\mathbf a_i$, reciprocal primitive vectors satisfy $\mathbf a_i\cdot\mathbf b_j=2\pi\delta_{ij}$, and $\mathbf G=\sum_jn_j\mathbf b_j$ for integers $n_j$.
The <first Brillouin zone> is the <Wigner-Seitz cell> of that <reciprocal lattice>, centered at $\mathbf k=0$. Its boundaries are <Bragg planes>, $\mathbf k\cdot\mathbf G=G^2/2$. Higher <Brillouin zones> are the regions separated from the origin by successively more such planes: an interior point of zone $j$ has crossed exactly $j-1$ planes. A <second Brillouin zone> is generally disconnected in this extended-zone representation; it is not just a translated first-zone rectangle.
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