Dense Packings of Rounded Tetrahedra in Cylindrical Confinement

From the stacking of cannonballs in the Kepler conjecture to the formation of virus capsids, descriptions of dense packings of discrete objects explain phenomena at a variety of length scales. Here we use hard particle Monte Carlo methods to study dense packing configurations of a family of hard tetrahedral shapes confined within cylinders. We present methods for generating these packings, varying the confining cylinder diameter, particle shape, and a boundary twist angle. This twist angle allows us to generate and define structures with a fundamental cell that repeats with an irrational twist rotation along the length of the cylinder, such as the Coxeter-Boerdijk tetrahelix. In additional to the tetrahelix, we observe a variety of structures in the packing landscape: achiral stacks of tetrahedral dimer clusters; simple, double, and triple helices; and columnar packings observed in dodecagonal quasicrystals. As we interpolate between tetrahedra and spheres, we see a peak in packing density at an intermediate value of rounding. The location of this peak is highly sensitive to the diameter of the cylinder. The tunable chirality of our dense packings serves as a exciting guide for precise synthesis of novel self-assembled chiral superstructures.