Reciprocal lattice and Wigner-Seitz cell of the unit triangular lattice
= Reciprocal lattice and Wigner-Seitz cell of the unit triangular lattice
For direct primitive vectors $(1,0)$ and $(-1/2,\sqrt3/2)$, reciprocal primitive vectors are
$$
\left(2\pi,\frac{2\pi}{\sqrt3}\right),
\qquad
\left(0,\frac{4\pi}{\sqrt3}\right).
$$
The reciprocal Wigner--Seitz cell is a regular hexagon of area $8\pi^2/\sqrt3$ and circumradius $4\pi/3$.