Cubic lattice knots: 6_1, 6_2 and 6_3

2023-08-23 21:47:14

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Summary

The 6_1, 6_2 and 6_3 knots constructed so that their vertices lie on the cubic lattice. (The cubic lattice is the set of all points in 3-dimensional space where each of the three coordinates is an integer.)

These knots were created by Chadrack Bantange and JCW (students in Math 383D Knot Theory Spring 2023).

A description of how these knots were built can be found here: https://mathvis.academic.wlu.edu/2023/05/19/tying-knots-on-the-shortest-lattice-walks/

The data for the vertices of these knots is from Andrew Rechnitzer’s website found here: https://personal.math.ubc.ca/~andrewr/knots/minimal_knots.html This data is from the research paper: E.J. Janse van Rensburg and A. Rechnitzer
Minimal knotted polygons in cubic lattices
Journal of Statistical Mechanics: Theory and Experiment: P09008 (2011).