Chern Chuang
Accompanying the manuscript titled "Torus Knots with Polygonal Faces" submitted to the Bridges 2014, here we present two enantiomeric and perhaps iconic carbon nanotube trefoil knots made of crystal beads. The beading technique follows what we (Prof. Bih-Yaw Jin at National Taiwan University and the current author) have been promoting throughout the past few Bridges. Simply put, we replace each of the chemical bonds in a molecule by a bead and trace out a connected graph of the molecule with fish line. In most cases visited the graphs are Hamiltonian, and all constituent beads will be threaded exactly twice. Please refer to our manuscript for detail.
The C318 carbon nanotube trefoil knot is the most elegant one in its family found by the authors. The elegance reveals itself both from the aesthetic and from mechanical points of view, that the size-to-radius ratio fits neatly with the most common rendering of a trefoil knot, with minimal carbon atoms involved.