$\sigma_0:$
$\sigma_1:$
$\sigma_2:$
$\sigma_3:$
$\sigma_4:$
$\sigma_5:$
$\sigma_6:$
$\sigma_7:$
$\sigma_8:$
$\sigma_9:$
$\text{plane}_1:$
$\text{plane}_2:$
$\text{plane}_3:$
$v_i:$

$\colorbox{#FFFFFF}{$\sigma_0$} = \langle v_1, v_2, v_3 \rangle$
$\colorbox{#FFFF7F}{$\sigma_1$} = \langle v_1, v_2, v_7 \rangle$
$\colorbox{#FF7FFF}{$\sigma_2$} = \langle v_1, v_3, v_6 \rangle$
$\colorbox{#7FFFFF}{$\sigma_3$} = \langle v_1, v_6, v_7 \rangle$
$\colorbox{#FF7F7F}{$\sigma_4$} = \langle v_2, v_3, v_5 \rangle$
$\colorbox{#7FFF7F}{$\sigma_5$} = \langle v_2, v_5, v_7 \rangle$
$\colorbox{#7F7FFF}{$\sigma_6$} = \langle v_3, v_5, v_6 \rangle$
$\colorbox{#7F7F7F}{$\sigma_7$} = \langle v_4, v_5, v_6 \rangle$
$\colorbox{#7F7F00}{$\sigma_8$} = \langle v_4, v_5, v_7 \rangle$
$\colorbox{#7F007F}{$\sigma_9$} = \langle v_4, v_6, v_7 \rangle$
$v_1 = (1, 0, 0)$
$v_2 = (0, 1, 0)$
$v_3 = (0, 0, 1)$
$v_4 = (-1, -1, -1)$
$v_5 = (-1, -1, 0)$
$v_6 = (0, -1, -1)$
$v_7 = (-1, 0, -1)$