Cinquefoil knot
In knot theory, the cinquefoil knot, also known as Solomon's seal knot or the pentafoil knot, is one of two knots with crossing number five, the other being the three-twist knot. It is listed as the 51 knot in the Alexander-Briggs notation, and can also be described as the (5,2)-torus knot. The cinquefoil is the closed version of the double overhand knot.
| Cinquefoil | |
|---|---|
| Common name | Double overhand knot |
| Arf invariant | 1 |
| Braid length | 5 |
| Braid no. | 2 |
| Bridge no. | 2 |
| Crosscap no. | 1 |
| Crossing no. | 5 |
| Genus | 2 |
| Hyperbolic volume | 0 |
| Stick no. | 8 |
| Unknotting no. | 2 |
| Conway notation | [5] |
| A–B notation | 51 |
| Dowker notation | 6, 8, 10, 2, 4 |
| Last / Next | 41 / 52 |
| Other | |
| alternating, torus, fibered, prime, reversible | |
This article is issued from Wikipedia. The text is licensed under Creative Commons - Attribution - Sharealike. Additional terms may apply for the media files.