Year: 2026
Type: preprint
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.
Source: arXiv (Cornell University)
Institutions: University of Michigan, Aberystwyth University
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funders: National Science Foundation, U.S. Department of Energy, Purdue University, Office of Science, U.S. Navy, Engineering and Physical Sciences Research Council, Office of Naval Research, Division of Materials Research, Office of Advanced Cyberinfrastructure, Division of Mathematical Sciences, Advanced Scientific Computing Research
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