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

Root polytopes and growth series of root lattices