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Porous materials made up of impermeable polyhedral grains constrain fluidflow to voids around the impenetrable constituent barrier particles. Apercolation transition marks the boundary between assemblies of grains whichcontain system spanning void networks, admitting bulk transport, andconfigurations which may not be traversed on macroscopic scales. With dynamicalinfiltration of void spaces using virtual tracer particles, we give an exacttreatment of grain geometries, and we calculate critical densities forpolyhedral inclusions for the five platonic solids (i.e. tetrahedra, cubes,octahededra, dodecahedra, and icosahedra). In each case, we calculatepercolation threshold concentrations $\rho_{c}$ for aligned and randomlyoriented grains, finding distinct $\rho_{c}$ values for the former versus thelatter only for cube-shaped grains. We calculate the dynamical scaling exponentat the percolation threshold, finding subdiffusive value $z = 0.19(1)$ commonto all grain shapes considered.

Percolation through Voids around Randomly Oriented Platonic Solids