$\large \vec{k}=u\vec{b}_1+v\vec{b}_2+w\vec{b}_3\,:\,(u,v,w)$  Symmetry points $(u,v,w)$  $[k_x,k_y,k_z]$   Point group    $\Gamma:\,(0,0,0)$   $[0,0,0]$ mmm  $Y:\, (\frac{1}{2},\frac{1}{2},0)$   $[\frac{\pi}{a},0,0]$  mmm  $Y':\, (-\frac{1}{2},\frac{1}{2},0)$   $[0,\frac{\pi}{b},0]$  mmm  $Z:\, (0,0,\frac{1}{2})$   $[0,0,\frac{\pi}{c}]$  mmm  $T:\, (\frac{1}{2},\frac{1}{2},\frac{1}{2})$   $[\frac{\pi}{a},0,\frac{\pi}{c}]$  mmm  $T':\, (-\frac{1}{2},\frac{1}{2},\frac{1}{2})$   $[0,\frac{\pi}{b},\frac{\pi}{c}]$  mmm  $S:\, (0,\frac{1}{2},0)$   $[\frac{\pi}{2a},\frac{\pi}{2b},0]$ 2/m  $R:\, (0,\frac{1}{2},\frac{1}{2})$   $[\frac{\pi}{2a},\frac{\pi}{2b},\frac{\pi}{c}]$ 2/m   $\overline{\Gamma Y} = \frac{\pi}{a}$ $\overline{\Gamma Z} = \overline{YT}= \overline{SR}= \frac{\pi}{c}$ $\overline{\Gamma T} = \frac{\pi}{ac}\sqrt{a^2+c^2}$    Symmetry lines    Point group    $\Lambda :\,(0,0,w)$ $ 0\lt w\lt\frac{1}{2}$  mm2  $H :\,(\frac{1}{2},\frac{1}{2},w)$ $ 0\lt w\lt\frac{1}{2}$  mm2  $\Sigma :\,(u,u,0)$ $ 0\lt u\lt\frac{1}{2}$  mm2  $A :\,(u,u,\frac{1}{2})$ $ 0\lt u\lt\frac{1}{2}$  mm2  $\Delta :\,(-v,v,0)$ $ 0\lt v\lt\frac{(a^2+b^2)}{4a^2}$  mm2  $B :\,(-v,v,\frac{1}{2})$ $ 0\lt v\lt\frac{(a^2+b^2)}{4a^2}$  mm2  $F :\,(\frac{1}{2}-v,\frac{1}{2}+v,0)$ $ 0\lt v\lt\frac{1}{2}-\frac{(a^2+b^2)}{4a^2}$  mm2  $G :\,(\frac{1}{2}-v,\frac{1}{2}+v,\frac{1}{2})$ $ 0\lt v\lt\frac{1}{2}-\frac{(a^2+b^2)}{4a^2}$  mm2  $D :\,(0,\frac{1}{2},w)$ $ 0\lt w\lt\frac{1}{2}$  2

The real space and reciprocal space primitive translation vectors are:

$\large \vec{a}_1 = \frac{a}{2} \hat{x}-\frac{b}{2}\hat{y}$  $\large \vec{a}_2 = \frac{a}{2} \hat{x}+\frac{b}{2}\hat{y} $  $\large \vec{a}_3 = c\hat{z}$,

$\large \vec{b}_1 = \frac{2\pi}{a}\hat{k_x}-\frac{2\pi}{b}\hat{k_y}$  $\large \vec{b}_2 =\frac{2\pi}{a}\hat{k_x}+\frac{2\pi}{b}\hat{k_y}$  $\large \vec{b}_3 = \frac{2\pi}{c}\hat{k_z}$.

Cut-out pattern to make a paper model of the body centered orthorhombic Brillouin zone.