  Let $\Phi$ be an irreducible crystallographic root system and $\mathcal P$
its root polytope, i.e., its convex hull. We provide a uniform construction,
for all root types, of a triangulation of the facets of $\mathcal P$. We also
prove that, on each orbit of facets under the action of the Weyl gruop, the
triangulation is unimodular with respect to a root sublattice that depends on
the orbit.
