A3 root system (source code)

= A3 root system
{c}
{title2=$A_3$}

The $A_3$ root system is $\{e_i-e_j:1\leq i\ne j\leq4\}$ in the hyperplane of $\mathbb R^4$ whose coordinates sum to zero. It has $12$ roots and simple roots $e_1-e_2,e_2-e_3,e_3-e_4$.