Random sequential adsorption of Platonic and Archimedean solids.

Abstract

The aim of this study is the analysis of packings generated according to random sequential adsorption protocol consisting of identical Platonic and Archimedean solids. The computer simulations performed showed that the highest saturated packing fraction θ=0.40210(68) is reached by packings build of truncated tetrahedra and the smallest one θ=0.35635(67) by packings composed of regular tetrahedra. The propagation of translational and orientational order exhibited microstructural properties typically seen in random sequential adsorption packings and the kinetics of three-dimensional packings growth were again observed not to be strictly connected with the dimension of the configuration space. Moreover, a fast overlap criterion for Platonic and Archimedean solids based on separating axis theorem has been described. The criterion, together with other optimizations, allowed us to generate significantly larger packings, which translated directly to a lower statistical error of the results obtained. Additionally, the polyhedral order parameters provided can be utilized in other studies regarding particles of polyhedral symmetry.