  This paper proves a "new" family of functional equations (Eqn) for Rogers
dilogarithm. These equations rely on the combinatorics of dihedral coordinates
on moduli spaces of curves of genus 0, M 0,n. For n = 4 we find back the
duality relation while n = 5 gives back the 5 terms relation. It is then proved
that the whole family reduces to the 5 terms relation. In the author's
knownledge, it is the first time that an infinite family of functional
equations for the dilogarithm with an increasing number of variables (n -- 3
for (Eqn)) is reduced to the 5 terms relation.
