Dense crystalline dimer packings of regular tetrahedra

Abstract

We present the densest known packing of regular tetrahedra with density phi = 4000/4671 = 0.856347... Like the recently discovered packings of Kallus et al. [arXiv:0910.5226] and Torquato-Jiao [arXiv:0912.4210], our packing is crystalline with a unit cell of four tetrahedra forming two triangular dipyramids (dimer clusters). We show that our packing has maximal density within a three-parameter family of dimer packings. Numerical compressions starting from random configurations suggest that the packing may be optimal at least for small cells with up to 16 tetrahedra and periodic boundaries.

43 pages, revision of the proofs and the appendices, data for small unit cell packings in appendix D

References in corpus (8)

• Disordered, Quasicrystalline and Crystalline Phases of Densely Packed Tetrahedra
• Dense Packings of the Platonic and Archimedean Solids
• Dense Packings of Polyhedra: Platonic and Archimedean Solids
• Dense crystalline dimer packings of regular tetrahedra
• Exact Constructions of a Family of Dense Periodic Packings of Tetrahedra
• Dense periodic packings of tetrahedra with small repeating units
• A Dense Packing of Regular Tetrahedra
• Analytical Constructions of a Family of Dense Tetrahedron Packings and the Role of Symmetry

Cited by in corpus (37)

• Jammed Hard-Particle Packings: From Kepler to Bernal and Beyond
• Crystalline Assemblies and Densest Packings of a Family of Truncated Tetrahedra and the Role of Directional Entropic Forces
• Dense Regular Packings of Irregular Non-Convex Particles
• Basic Understanding of Condensed Phases of Matter via Packing Models
• Maximum and Minimum Stable Random Packings of Platonic Solids
• Dense crystalline dimer packings of regular tetrahedra
• Phase Diagram of Hard Tetrahedra
• Densest binary sphere packings
• Incompressibility of polydisperse random close packed colloidal particles
• Jammed frictional tetrahedra are hyperstatic
• Equilibrium Phase Behavior and Maximally Random Jammed State of Truncated Tetrahedra
• Degenerate Quasicrystal of Hard Triangular Bipyramids
• Organizing Principles for Dense Packings of Nonspherical Hard Particles: Not All Shapes Are Created Equal
• Athermal jamming of soft frictionless Platonic solids
• Hyperuniformity, quasi-long-range correlations, and void-space constraints in maximally random jammed particle packings. II. Anisotropy in particle shape
• Complexity in surfaces of densest packings for families of polyhedra
• Isostaticity of Constraints in Jammed Systems of Soft Frictionless Platonic Solids
• Differently Shaped Hard Body Colloids in Confinement: From passive to active particles
• Dense packing crystal structures of physical tetrahedra
• Packing and Self-assembly of Truncated Triangular Bipyramids
• Upper bound on the packing density of regular tetrahedra and octahedra
• Self-assembly of a space-tessellating structure in the binary system of hard tetrahedra and octahedra
• Novel dense crystalline packings of ellipsoids
• New upper bounds for the density of translative packings of three-dimensional convex bodies with tetrahedral symmetry
• Dense periodic packings of tori
• Varieties of mathematical understanding
• Hard convex lens-shaped particles: Characterization of dense disordered packings
• A method for dense packing discovery
• Geometrical properties of rigid frictionless granular packings as a function of particle size and shape
• Computing upper bounds for the packing density of congruent copies of a convex body
• Cuddling Ellipsoids: Densest local structures of uniaxial ellipsoids
• Mathematical optimization for packing problems
• Upper bound on the disordered density of sphere packing and the Kepler Conjecture
• On the translative packing densities of tetrahedra and cubooctahedra
• Errata and Addenda to Mathematical Constants
• On the minimal area of quadrangles circumscribed about planar convex bodies
• Golden, Quasicrystalline, Chiral Packings of Tetrahedra