= Triple bond isolates a G2 component
If two <simple roots> have angle $5\pi/6$, normalize them to unit vectors $u,v$ with $(u,v)=-\sqrt3/2$. For any other unit <simple root> $w$, set $r=(u,w)\le0$, $s=(v,w)\le0$. Its three-root <Gram matrix> has determinant $1/4-r^2-s^2-\sqrt3rs$. Any nonzero $r$ or $s$ has absolute value at least $1/2$, contradicting positive definiteness. Thus all other <simple roots> are orthogonal to $u,v$. An irreducible <root system> containing this triple bond must be the rank-two <G2 root system>.
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