Dense packing crystal structures of physical tetrahedra

TL;DR

This paper introduces a method to discover dense packings of convex particles, applying it to a family of tetrahedral shapes, revealing diverse optimal structures bridging sphere and tetrahedron packings.

Contribution

It develops a new approach for dense packing discovery and explores the packing behavior of deformable tetrahedral particles, connecting sphere and tetrahedron packing problems.

Findings

Identified four candidate structures for optimal packing at different particle shapes.

Revealed a rich variety of packing behaviors compared to previous studies.

Connected sphere packing and tetrahedron packing through a continuous deformation parameter.

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.