# Non-Close-Packed Three-Dimensional Quasicrystals

## TL;DR

This study demonstrates the computational self-assembly of four distinct three-dimensional quasicrystals, including known and novel structures, using a single model system with tunable isotropic interactions, revealing diverse phases such as network gels.

## Contribution

It introduces the first computational demonstration of multiple 3D quasicrystals forming in a unified model system with isotropic pair potentials, including new decagonal, dodecagonal, and octagonal phases.

## Key findings

- Reproduced known icosahedral quasicrystal.
- Discovered decagonal, dodecagonal, and octagonal quasicrystals.
- Identified a network gel phase.

## Abstract

Quasicrystals are frequently encountered in condensed matter. They are important candidates for equilibrium phases from the atomic scale to the nanoscale. Here, we investigate the computational self-assembly of four quasicrystals in a single model system of identical particles interacting with a tunable isotropic pair potential. We reproduce a known icosahedral quasicrystal and report a decagonal quasicrystal, a dodecagonal quasicrystal, and an octagonal quasicrystal. The quasicrystals have low coordination number or occur in systems with mesoscale density variations. We also report a network gel phase.