Random packing of regular polygons and star polygons on a flat two-dimensional surface

TL;DR

This study numerically investigates the random packing behavior of regular polygons and star polygons on a 2D surface, analyzing packing ratios, autocorrelation, and kinetics to understand how shape influences packing efficiency.

Contribution

It introduces a numerical analysis of packing properties for polygons and star polygons, revealing how shape and vertex count affect packing density and similarity to disks.

Findings

Stars have lower packing ratios than polygons.

Large vertex count shapes approach disk packing properties.

Packing properties depend on shape and vertex number.

Abstract

Random packing of unoriented regular polygons and star polygons on a two-dimensional flat, continuous surface is studied numerically using random sequential adsorption algorithm. Obtained results are analyzed to determine saturated random packing ratio as well as its density autocorrelation function. Additionally, the kinetics of packing growth and available surface function are measured. In general, stars give lower packing ratios than polygons, but, when the number of vertexes is large enough, both shapes approach disks and, therefore, properties of their packing reproduce already known results for disks.