Reciprocal lattice and Wigner-Seitz cell of the unit triangular lattice

For direct primitive vectors $(1,0)$ and $(-1/2,\sqrt{3}/2)$, reciprocal primitive vectors areThe reciprocal Wigner--Seitz cell is a regular hexagon of area $8{\pi }^2/\sqrt{3}$ and circumradius $4\pi /3$.