Reciprocal lattice
= Reciprocal lattice
{title2=$\Lambda^*$}
{wiki}
The reciprocal lattice is
$$
\Lambda^*=\{q:q\cdot l\in2\pi\mathbb Z\text{ for every }l\in\Lambda\}.
$$
If $\Omega=a_1\cdot(a_2\times a_3)$, its primitive vectors are
$$
b_1=2\pi\frac{a_2\times a_3}{\Omega},
\quad
b_2=2\pi\frac{a_3\times a_1}{\Omega},
\quad
b_3=2\pi\frac{a_1\times a_2}{\Omega},
$$
and satisfy $a_i\cdot b_j=2\pi\delta_{ij}$.