  We describe the use of pyramid decomposition in Normaliz, a software tool for
the computation of Hilbert bases and enumerative data of rational cones and
affine monoids. Pyramid decomposition in connection with efficient
parallelization and streamlined evaluation of simplicial cones has enabled
Normaliz to process triangulations of size $\approx 5\cdot 10^{11}$ that arise
in the computation of Hilbert series related to combinatorial voting theory.
