= Branching from B3 to A3
{title2=$\mathbf7\mapsto\mathbf6\oplus\mathbf1,\quad\mathbf8\mapsto\mathbf4\oplus\overline{\mathbf4}$}
For <B3 root system> <simple roots> $e_1-e_2,e_2-e_3,e_3$, choose the <D3 root system> <simple roots> in chain order $e_2-e_3,e_1-e_2,e_2+e_3$. The <Dynkin labels> project by $(a,b,c)\mapsto(b,a,b+c)$. This separates the vector <weights> $\{0,\pm e_i\}$ into the six-dimensional <exterior square> of the defining <SU(4)> <representation> and a <singlet representation>. The spinor cube vertices $\tfrac12(\pm e_1\pm e_2\pm e_3)$ split into its defining <representation> and its <dual representation>.
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