Virtual Knot 4.5
- This virtual knot is not equivalent to its vertical mirror image.
- This virtual knot is not equivalent to its horizontal mirror image.
- The two mirror images are not equivalent to each other.
- This virtual knot is not equivalent to its inverse.
- Gauss code
- O1-O2-U1-U2-O3+U4-U3+O4-
- PD presentation
- PD[X[2,8,3,1], X[3,1,4,2], X[6,5,7,4], X[5,7,6,8]]
- Jones polynomial
- - q-5/2 + q-3/2 + q-1
- Other virtual knots (up to mirrors) with the same Jones polynomial
- 2.1, 3.3, 4.4, 4.11, 4.18, 4.28, 4.30, 4.33, 4.38, 4.39, 4.44, 4.45, 4.49, 4.54, 4.62, 4.63, 4.74, 4.83, 4.95, 4.101
- Cabled Jones polynomials
- - q-15/2 + q-13/2 + q-11/2 + q-9/2 - q-7/2 - 2q-5/2 - q-1/2
- - q-29/2 - 5q-27/2 - 17q-13 - 32q-25/2 - 47q-12 - 65q-23/2 - 83q-11 - 94q-21/2 - 85q-10 - 64q-19/2 - 22q-9 + 38q-17/2 + 101q-8 + 160q-15/2 + 197q-7 + 206q-13/2 + 177q-6 + 118q-11/2 + 51q-5 - 11q-9/2 - 68q-4 - 97q-7/2 - 105q-3 - 91q-5/2 - 68q-2 - 49q-3/2 - 23q-1 - 13q-1/2 - 4 - 2q1/2 + 2q3/2
- Other virtual knots (up to mirrors) with the same cabled Jones polynomials
- none
- Generalized Alexander polynomial
- (- s-3 + s-1) t-2 + (s-3 + 2s-2 - 2s-1 - 1) t-1 + (- 2s-2 + 2) + (s-1 - 1) t
- Other virtual knots (up to mirrors/inversion) with the same Generalized Alexander polynomial
- 4.4, 4.30, 4.54, 4.74
- Self linking number
- -2