# Random sequential adsorption of Platonic and Archimedean solids

## TL;DR

This study investigates the packing behavior of Platonic and Archimedean solids using random sequential adsorption, revealing optimal packing fractions, microstructural properties, and improvements in simulation algorithms for larger packings.

## Contribution

It introduces optimized RSA algorithms for polyhedral packings and analyzes their structural and kinetic properties, providing new insights into polyhedral packing behavior.

## Key findings

- Highest packing fraction: 0.40210 for truncated tetrahedra
- Smallest packing fraction: 0.35635 for regular tetrahedra
- Optimized algorithms enable larger packings with reduced statistical error

## Abstract

The aim of the study presented here was 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 ${\theta}=0.40210(68)$ is reached by packings built of truncated tetrahedra and the smallest one ${\theta}=0.35635(67)$ by packings composed of regular tetrahedra. The propagation of translational and orientational order exhibited microstructural propertied typically seen in RSA packings and the kinetics of 3 dimensional packings growth were again observed not to be strictly connected with the dimenstion of the configuration space. Moreover, a number of optimizations for the RSA algorithm were described allowing generation of 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.