  The convex hull of the roots of a classical root lattice is called a root
polytope. We determine explicit unimodular triangulations of the boundaries of
the root polytopes associated to the root lattices A_n, C_n, and D_n, and
compute their f-and h-vectors. This leads us to recover formulae for the growth
series of these root lattices, which were first conjectured by
Conway-Mallows-Sloane and Baake-Grimm and proved by Conway-Sloane and Bacher-de
la Harpe-Venkov.
