I have been reading up on knots recently, so here is a table of 8 knots with up to 6 crossings (plus 2 extras), along with their Conway polynomials. These are polynomials that can be associated with each knot. Different polynomials imply different knots, but sometimes different knots have the same polynomial. Some examples are shown in red below. I have also included pictures of the ten knots mentioned (not drawn by me).
| Knot | Conway polynomial |
|---|---|
| 01 (Unknot) | 1 |
| 31 (Trefoil knot) | z2 + 1 |
| 41 (Figure-eight knot) | 1 − z2 |
| 51 (Cinquefoil knot) | z4 + 3 z2 + 1 |
| 52 (Three-twist knot) | 2 z2 + 1 |
| 61 (Stevedore’s knot) | 1 − 2 z2 |
| 62 (Miller Institute knot) | − z4 − z2 + 1 |
| 63 | z4 + z2 + 1 |
| 946 | 1 − 2 z2 |
| 10132 | z4 + 3 z2 + 1 |
Scientific Gems 