| Min(phi) over symmetries of the knot is: [-3,-2,1,1,1,2,0,2,3,3,2,1,1,2,1,1,-1,1,-1,1,2] |
| Flat knots (up to 7 crossings) with same phi are :['6.749'] |
| Arrow polynomial of the knot is: -8*K1**2 - 2*K1*K2 + K1 + 4*K2 + K3 + 5 |
| Flat knots (up to 7 crossings) with same arrow polynomial are :['6.377', '6.638', '6.646', '6.647', '6.657', '6.658', '6.662', '6.692', '6.695', '6.714', '6.720', '6.726', '6.730', '6.731', '6.749', '6.756', '6.772', '6.779', '6.781', '6.800', '6.829', '6.1085', '6.1089', '6.1302', '6.1349', '6.1350', '6.1360', '6.1362', '6.1375', '6.1384'] |
| Outer characteristic polynomial of the knot is: t^7+62t^5+105t^3+4t |
| Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.749'] |
| 2-strand cable arrow polynomial of the knot is: -64*K1**6 + 160*K1**4*K2 - 2032*K1**4 + 32*K1**3*K2*K3 - 160*K1**3*K3 + 128*K1**2*K2**3 - 3488*K1**2*K2**2 - 128*K1**2*K2*K4 + 6264*K1**2*K2 - 560*K1**2*K3**2 - 48*K1**2*K4**2 - 3660*K1**2 - 832*K1*K2**2*K3 + 4992*K1*K2*K3 + 968*K1*K3*K4 + 40*K1*K4*K5 - 224*K2**4 - 160*K2**2*K3**2 - 8*K2**2*K4**2 + 560*K2**2*K4 - 3086*K2**2 + 120*K2*K3*K5 + 8*K2*K4*K6 - 1544*K3**2 - 344*K4**2 - 28*K5**2 - 2*K6**2 + 3094 |
| Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.749'] |
| Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.11521', 'vk6.11852', 'vk6.12867', 'vk6.13174', 'vk6.20360', 'vk6.21703', 'vk6.27660', 'vk6.29206', 'vk6.31296', 'vk6.31691', 'vk6.32450', 'vk6.32865', 'vk6.39102', 'vk6.41358', 'vk6.45854', 'vk6.47517', 'vk6.52304', 'vk6.52568', 'vk6.53144', 'vk6.53448', 'vk6.57219', 'vk6.58442', 'vk6.61829', 'vk6.62962', 'vk6.63813', 'vk6.63945', 'vk6.64255', 'vk6.64451', 'vk6.66832', 'vk6.67702', 'vk6.69468', 'vk6.70192'] |
| The R3 orbit of minmal crossing diagrams contains: |
| The diagrammatic symmetry type of this knot is c. |
| The reverse -K is |
| The mirror image K* is |
| The reversed mirror image -K* is |
| The fillings (up to the first 10) associated to the algebraic genus: |
| Or click here to check the fillings |
| invariant | value |
|---|---|
| Gauss code | O1O2O3O4U2O5U3U6U1O6U5U4 |
| R3 orbit | {'O1O2O3O4U2O5U3U6U1O6U5U4'} |
| R3 orbit length | 1 |
| Gauss code of -K | O1O2O3O4U1U5O6U4U6U2O5U3 |
| Gauss code of K* | O1O2O3U2O4O5U3U6U1U5O6U4 |
| Gauss code of -K* | O1O2O3U4O5U6U3U5U1O6O4U2 |
| Diagrammatic symmetry type | c |
| Flat genus of the diagram | 3 |
| If K is checkerboard colorable | False |
| If K is almost classical | False |
| Based matrix from Gauss code | [[ 0 -1 -2 -1 3 2 -1],[ 1 0 -1 1 3 1 1],[ 2 1 0 1 2 1 2],[ 1 -1 -1 0 2 1 1],[-3 -3 -2 -2 0 0 -3],[-2 -1 -1 -1 0 0 -2],[ 1 -1 -2 -1 3 2 0]] |
| Primitive based matrix | [[ 0 3 2 -1 -1 -1 -2],[-3 0 0 -2 -3 -3 -2],[-2 0 0 -1 -1 -2 -1],[ 1 2 1 0 -1 1 -1],[ 1 3 1 1 0 1 -1],[ 1 3 2 -1 -1 0 -2],[ 2 2 1 1 1 2 0]] |
| If based matrix primitive | True |
| Phi of primitive based matrix | [-3,-2,1,1,1,2,0,2,3,3,2,1,1,2,1,1,-1,1,-1,1,2] |
| Phi over symmetry | [-3,-2,1,1,1,2,0,2,3,3,2,1,1,2,1,1,-1,1,-1,1,2] |
| Phi of -K | [-2,-1,-1,-1,2,3,-1,0,0,3,3,1,1,1,1,-1,2,1,2,2,1] |
| Phi of K* | [-3,-2,1,1,1,2,1,1,1,2,3,1,2,2,3,-1,-1,-1,1,0,0] |
| Phi of -K* | [-2,-1,-1,-1,2,3,1,1,2,1,2,-1,1,1,2,1,1,3,2,3,0] |
| Symmetry type of based matrix | c |
| u-polynomial | -t^3+3t |
| Normalized Jones-Krushkal polynomial | 3z^2+20z+29 |
| Enhanced Jones-Krushkal polynomial | 3w^3z^2+20w^2z+29w |
| Inner characteristic polynomial | t^6+42t^4+43t^2 |
| Outer characteristic polynomial | t^7+62t^5+105t^3+4t |
| Flat arrow polynomial | -8*K1**2 - 2*K1*K2 + K1 + 4*K2 + K3 + 5 |
| 2-strand cable arrow polynomial | -64*K1**6 + 160*K1**4*K2 - 2032*K1**4 + 32*K1**3*K2*K3 - 160*K1**3*K3 + 128*K1**2*K2**3 - 3488*K1**2*K2**2 - 128*K1**2*K2*K4 + 6264*K1**2*K2 - 560*K1**2*K3**2 - 48*K1**2*K4**2 - 3660*K1**2 - 832*K1*K2**2*K3 + 4992*K1*K2*K3 + 968*K1*K3*K4 + 40*K1*K4*K5 - 224*K2**4 - 160*K2**2*K3**2 - 8*K2**2*K4**2 + 560*K2**2*K4 - 3086*K2**2 + 120*K2*K3*K5 + 8*K2*K4*K6 - 1544*K3**2 - 344*K4**2 - 28*K5**2 - 2*K6**2 + 3094 |
| Genus of based matrix | 1 |
| Fillings of based matrix | [[{1, 6}, {3, 5}, {2, 4}], [{1, 6}, {4, 5}, {2, 3}], [{5, 6}, {3, 4}, {1, 2}]] |
| If K is slice | False |