  Random tessellations of the space represent a class of prototype models of
heterogeneous media, which are central in several applications in physics,
engineering and life sciences. In this work, we investigate the statistical
properties of $d$-dimensional isotropic Poisson geometries by resorting to
Monte Carlo simulation, with special emphasis on the case $d=3$. We first
analyse the behaviour of the key features of these stochastic geometries as a
function of the dimension $d$ and the linear size $L$ of the domain. Then, we
consider the case of Poisson binary mixtures, where the polyhedra are assigned
two `labels' with complementary probabilities. For this latter class of random
geometries, we numerically characterize the percolation threshold, the strength
of the percolating cluster and the average cluster size.
