Mosaic knots: 3#1, 4#1 and 7#1

Mosaic knots: 3_1, 4_1 and 7_1

2023-08-23 22:28:14

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Summary

The 3_1 trefoil, 4_1 figure 8, and 7_1 mosaic knots created by Sion Jang and Charlotte Peete (students in Math 383D Knot Theory Spring 2023). There are two stl files for the 7_1 knot, where the diameter and overall size of the knot is slightly different in each.

A mosaic knot is a knot built out of a combination of 11 tiles to create a representation for a knot on an nxn grid. The smallest n for which a particular knot can be represented on a mosaic board is called the mosaic number. The 11 mosaic tiles and minimal grid mosaic knot diagrams can be found in the paper Knot mosaic tabulation by Hwa Jeong Lee, Lew Ludwig, Joseph Paat and Amanda Peiffer in Involve vol.11 No. 1, 13-26 (2018) https://msp.org/involve/2018/11-1/involve-v11-n1-p02-p.pdf The following blog post also describes the math: https://mathvis.academic.wlu.edu/2023/05/17/3d-printed-trefoil-mosaic-knot/