6₂ knot
| 6₂ knot | |
|---|---|
 |
|
| Arf invariant | 1 |
| Braid length | 6 |
| Braid no. | 3 |
| Bridge no. | 2 |
| Crosscap no. | 2 |
| Crossing no. | 6 |
| Genus | 2 |
| Hyperbolic volume | 4.40083 |
| Stick no. | 8 |
| Unknotting no. | 1 |
| Conway notation | [312] |
| A-B notation | 62 |
| Dowker notation | 4, 8, 10, 12, 2, 6 |
| Last /Next | 61 / 63 |
| Other | |
| alternating, hyperbolic, fibered, prime, reversible, twist | |
In knot theory, the 62 knot is one of three prime knots with crossing number six, the others being the stevedore knot and the 63 knot. This knot is sometimes referred to as the Miller Institute knot, because it appears in the logo of the Miller Institute for Basic Research in Science at the University of California, Berkeley.
The 62 knot is invertible but not amphichiral. Its Alexander polynomial is
its Conway polynomial is
and its Jones polynomial is
The 62 knot is a hyperbolic knot, with its complement having a volume of approximately 4.40083.
Surface of knot 6.2
Ways to assemble of knot 6.2
Example 1
Example 2
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Wikipedia