Dense packing crystal structures of physical tetrahedra

Abstract

We present a method for discovering dense packings of general convex hard particles and apply it to study the dense packing behavior of a one-parameter family of particles with tetrahedral symmetry representing a deformation of the ideal mathematical tetrahedron into a less ideal, physical, tetrahedron and all the way to the sphere. Thus, we also connect the two well studied problems of sphere packing and tetrahedron packing on a single axis. Our numerical results uncover a rich optimal-packing behavior, compared to that of other continuous families of particles previously studied. We present four structures as candidates for the optimal packing at different values of the parameter, providing an atlas of crystal structures which might be observed in systems of nano-particles with tetrahedral symmetry.

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Cited by in corpus (7)

• Crystalline Assemblies and Densest Packings of a Family of Truncated Tetrahedra and the Role of Directional Entropic Forces
• Organizing Principles for Dense Packings of Nonspherical Hard Particles: Not All Shapes Are Created Equal
• Maximally dense packings of two-dimensional convex and concave noncircular particles
• Complexity in surfaces of densest packings for families of polyhedra
• The random packing density of nearly spherical particles
• Packing and Self-assembly of Truncated Triangular Bipyramids
• Random sequential adsorption of Platonic and Archimedean solids