Screw symmetry in columnar crystals

Abstract

We show that the optimal packing of hard spheres in an infinitely long cylinder yields structures characterized by a screw symmetry. Each packing can be assembled by stacking a basic unit cell ad infinitum along the length of the cylinder with each subsequent unit cell rotated by the same twist angle with respect to the previous one. In this paper we quantitatively describe the nature of this screw operation for all such packings in the range and also briefly discuss their helicity.

Keywords:

• hard sphere packing
• screw symmetry
• phyllotaxis

Acknowledgments

AM acknowledges numerous useful discussions with Denis Weaire.