Three-twist knot
From Infogalactic: the planetary knowledge core
Three-twist knot | |
---|---|
Arf invariant | 0 |
Braid length | 6 |
Braid no. | 3 |
Bridge no. | 2 |
Crosscap no. | 2 |
Crossing no. | 5 |
Genus | 1 |
Hyperbolic volume | 2.82812 |
Stick no. | 8 |
Unknotting no. | 1 |
Conway notation | [32] |
A-B notation | 52 |
Dowker notation | 4, 8, 10, 2, 6 |
Last /Next | 51 / 61 |
Other | |
alternating, hyperbolic, prime, reversible, twist |
In knot theory, the three-twist knot is the twist knot with three-half twists. It is listed as the 52 knot in the Alexander-Briggs notation, and is one of two knots with crossing number five, the other being the cinquefoil knot.
The three-twist knot is a prime knot, and it is invertible but not amphichiral. Its Alexander polynomial is
its Conway polynomial is
and its Jones polynomial is
Because the Alexander polynomial is not monic, the three-twist knot is not fibered.
The three-twist knot is a hyperbolic knot, with its complement having a volume of approximately 2.82812.
References
- ↑ "5_2", The Knot Atlas.
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Categories:
- 0 Arf invariant knots and links
- 6 braid length knots and links
- 3 braid number knots and links
- 2 bridge number knots and links
- 2 crosscap number knots and links
- 5 crossing number knots and links
- 1 genus knots and links
- 8 stick number knots and links
- 1 unknotting number knots and links
- Alternating knots and links
- Hyperbolic knots and links
- Unfibered knots and links
- Twist knots
- Prime knots
- Reversible knots and links
- Non-tricolorable knots and links
- Knot theory stubs
- 2.82812 hyperbolic volume knots and links