On the Contact Numbers of Ball Packings on Various Hexagonal Grids

TL;DR

This paper studies the contact numbers of ball packings on various three-dimensional hexagonal grids, introduces notation for these grids, and presents computational results for packings of up to 200 balls using a greedy algorithm.

Contribution

It introduces a notation system for 3D hexagonal grids and investigates contact numbers of ball packings, including computational results up to 200 balls.

Findings

Contact numbers vary across different hexagonal grids.

Computational results for packings up to 200 balls are provided.

The octahedral grid is also analyzed.

Abstract

We describe the structure of the different hexagonal grids in dimension d=3, propose short notation for them, investigate the contact numbers of ball packings in these grids and share some computational results up to 200 balls, using mainly the greedy algorithm. We consider the octahedral grid, too.