# 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.

## Key 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.

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Source: https://tomesphere.com/paper/1901.07346