Virtual Knot 4.18
- 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-O3-U2+U4-U3-O4-
- PD presentation
- PD[X[2,8,3,1], X[4,2,5,1], X[6,3,7,4], 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, 4.5, 4.11, 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-17/2 + q-15/2 + q-13/2 - 2q-11/2 - 2q-9/2 - q-7/2 + q-3/2 - q-1/2
- - q-35/2 + 3q-33/2 - 4q-15 - 4q-29/2 - 14q-14 - 37q-27/2 - 64q-13 - 99q-25/2 - 122q-12 - 145q-23/2 - 132q-11 - 104q-21/2 - 31q-10 + 50q-19/2 + 135q-9 + 210q-17/2 + 239q-8 + 264q-15/2 + 231q-7 + 180q-13/2 + 106q-6 + 32q-11/2 - 23q-5 - 78q-9/2 - 111q-4 - 118q-7/2 - 112q-3 - 93q-5/2 - 69q-2 - 47q-3/2 - 21q-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-2 + s-1) t-2 + (s-2 - 1) t-1 + (- s-1 + 1)
- Other virtual knots (up to mirrors/inversion) with the same Generalized Alexander polynomial
- 2.1, 3.2, 3.4, 4.20, 4.27, 4.33, 4.34, 4.38, 4.40, 4.44, 4.49, 4.52, 4.60, 4.88, 4.94
- Self linking number
- -2