  Porous materials made up of impermeable polyhedral grains constrain fluid
flow to voids around the impenetrable constituent barrier particles. A
percolation transition marks the boundary between assemblies of grains which
contain system spanning void networks, admitting bulk transport, and
configurations which may not be traversed on macroscopic scales. With dynamical
infiltration of void spaces using virtual tracer particles, we give an exact
treatment of grain geometries, and we calculate critical densities for
polyhedral inclusions for the five platonic solids (i.e. tetrahedra, cubes,
octahededra, dodecahedra, and icosahedra). In each case, we calculate
percolation threshold concentrations $\rho_{c}$ for aligned and randomly
oriented grains, finding distinct $\rho_{c}$ values for the former versus the
latter only for cube-shaped grains. We calculate the dynamical scaling exponent
at the percolation threshold, finding subdiffusive value $z = 0.19(1)$ common
to all grain shapes considered.
