Golden, Quasicrystalline, Chiral Packings of Tetrahedra

TL;DR

This paper introduces a novel 'golden rotation' method to achieve perfect quasicrystalline packings of tetrahedra, improving upon previous dense but imperfect arrangements and advancing understanding of tetrahedral packing structures.

Contribution

The paper proposes a new 'golden rotation' technique to create perfect quasicrystalline packings of tetrahedra, surpassing prior semi-quasicrystalline arrangements.

Findings

A 'golden rotation' leads to perfect quasicrystalline packings.

The method results in higher packing density than previous approaches.

It provides a new geometric framework for tetrahedral packings.

Abstract

Since antiquity, the packing of convex shapes has been of great interest to many scientists and mathematicians. Recently, particular interest has been given to packings of three-dimensional tetrahedra. Dense packings of both crystalline and semi-quasicrystalline have been reported. It is interesting that a semiquasicrystalline packing of tetrahedra can emerge naturally within a thermodynamic simulation approach. However, this packing is not perfectly quasicrystalline and the packing density, while dense, is not maximal. Here we suggest that a "golden rotation" between tetrahedral facial junctions can arrange tetrahedra into a perfect quasicrystalline packing.