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

For direct primitive vectors

(1, 0)

and

(- 1/2, 3 /2)

, reciprocal primitive vectors are

(2 π, \frac{2 π}{3}), (0, \frac{4 π}{3}) .

The reciprocal Wigner--Seitz cell is a regular hexagon of area

8 π^{2} / 3

and circumradius

4 π /3

.

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