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PreprintCC BY 4.0arXiv

Dense Packing of Tetrahedra in Cylinders

  • Gabrielle N. Jones
  • Adil Mughal
  • Philipp W. A. Schönhöfer
  • Sharon C. Glotzer
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Abstract

We present the first systematic investigation of regular tetrahedra densely packed within a circular cylinder. Combining numerical simulations with exact analytical theory, we classify the densest configurations into two continuous, mathematically tractable families: chiral Tetra Helices and achiral Dimer Chains. Crucially, we reveal that the celebrated Boerdijk-Coxeter Helix is not an isolated anomaly, but a natural consequence of this cylindrical confinement. We further identify a striking symmetry-breaking bifurcation at a critical diameter, where the chiral helix coexists with an achiral dimer chain at a strictly identical packing fraction.

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Cite

BibTeXRIS
BibTeX
@misc{jones2026dense,
  title = {{Dense Packing of Tetrahedra in Cylinders}},
  author = {Gabrielle N. Jones and Adil Mughal and Philipp W. A. Schönhöfer and Sharon C. Glotzer},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.26627},
  eprint = {2609.26627},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.26627},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Dense Packing of Tetrahedra in Cylinders
AU  - Gabrielle N. Jones
AU  - Adil Mughal
AU  - Philipp W. A. Schönhöfer
AU  - Sharon C. Glotzer
PY  - 2026
DA  - 2026/09/22
PB  - arXiv
DO  - 10.48550/arxiv.2609.26627
UR  - https://arxiv.org/abs/2609.26627
AB  - We present the first systematic investigation of regular tetrahedra densely packed within a circular cylinder. Combining numerical simulations with exact analytical theory, we classify the densest configurations into two continuous, mathematically tractable families: chiral Tetra Helices and achiral Dimer Chains. Crucially, we reveal that the celebrated Boerdijk-Coxeter Helix is not an isolated anomaly, but a natural consequence of this cylindrical confinement. We further identify a striking symmetry-breaking bifurcation at a critical diameter, where the chiral helix coexists with an achiral dimer chain at a strictly identical packing fraction.
ER  -