  The descent algebra of a finite Coxeter group $W$ is a basic algebra, and as
such it has a presentation as quiver with relations. In recent work, we have
developed a combinatorial framework which allows us to systematically compute
such a quiver presentation for a Coxeter group of a given type. In this
article, we use that framework to determine quiver presentations for the
descent algebras of the Coxeter groups of exceptional or non-crystallographic
type, i.e., of type $E_6$, $E_7$, $E_8$, $F_4$, $H_3$, $H_4$ or $I_2(m)$.
