  For an affine toric variety X we compute the Poincare series of the
multi-index filtration defined by a finite number of monomial divisorial
valuations on the ring O_{X,0}. We give an alternative description of the
Poincare series as an integral with respect to the Euler characteristic over
the projectivization of the space of germs O_{X,0}. In particular we study
divisorial valuations on the ring O_{C^d,0} that arise by considering toric
constellations. We give an explicit formula for the Poincare series and a nice
geometric description. This generalizes an expression of the Poincare series
for curves and rational surface singularities.
