| Min(phi) over symmetries of the knot is: [-2,-1,0,1,1,1,0,1,1,1,2,0,0,1,0,1,1,1,1,-1,-1] |
| Flat knots (up to 7 crossings) with same phi are :['6.1485'] |
| Arrow polynomial of the knot is: -6*K1**2 - 4*K1*K2 + 2*K1 + 3*K2 + 2*K3 + 4 |
| Flat knots (up to 7 crossings) with same arrow polynomial are :['6.239', '6.428', '6.470', '6.556', '6.700', '6.910', '6.962', '6.1006', '6.1013', '6.1038', '6.1207', '6.1224', '6.1225', '6.1269', '6.1270', '6.1308', '6.1319', '6.1320', '6.1323', '6.1485', '6.1551', '6.1579', '6.1581', '6.1660', '6.1672', '6.1679', '6.1711', '6.1719', '6.1732', '6.1745', '6.1748', '6.1827', '6.1836', '6.1838', '6.1850', '6.1866'] |
| Outer characteristic polynomial of the knot is: t^7+32t^5+45t^3+4t |
| Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.1485'] |
| 2-strand cable arrow polynomial of the knot is: -64*K1**6 + 320*K1**4*K2 - 1856*K1**4 + 64*K1**3*K2*K3 - 768*K1**3*K3 + 128*K1**2*K2**3 - 2560*K1**2*K2**2 - 160*K1**2*K2*K4 + 6336*K1**2*K2 - 608*K1**2*K3**2 - 48*K1**2*K4**2 - 4372*K1**2 - 288*K1*K2**2*K3 - 160*K1*K2*K3*K4 + 4416*K1*K2*K3 + 1008*K1*K3*K4 + 96*K1*K4*K5 - 152*K2**4 - 96*K2**2*K3**2 - 48*K2**2*K4**2 + 408*K2**2*K4 - 3092*K2**2 + 144*K2*K3*K5 + 32*K2*K4*K6 - 1488*K3**2 - 406*K4**2 - 44*K5**2 - 4*K6**2 + 3260 |
| Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.1485'] |
| Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.11533', 'vk6.11864', 'vk6.12879', 'vk6.13186', 'vk6.20348', 'vk6.21691', 'vk6.27648', 'vk6.29194', 'vk6.31312', 'vk6.31707', 'vk6.32466', 'vk6.32881', 'vk6.39086', 'vk6.41342', 'vk6.45838', 'vk6.47505', 'vk6.52320', 'vk6.52580', 'vk6.53160', 'vk6.53460', 'vk6.57207', 'vk6.58426', 'vk6.61817', 'vk6.62946', 'vk6.63825', 'vk6.63957', 'vk6.64267', 'vk6.64463', 'vk6.66820', 'vk6.67690', 'vk6.69456', 'vk6.70180'] |
| 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 | O1O2O3U1O4U2U5O6O5U4U3U6 |
| R3 orbit | {'O1O2O3U1O4U2U5O6O5U4U3U6'} |
| R3 orbit length | 1 |
| Gauss code of -K | O1O2O3U4U1U5O6O4U6U2O5U3 |
| Gauss code of K* | O1O2O3U4U5U2O4U1O5O6U3U6 |
| Gauss code of -K* | O1O2O3U4U1O4O5U3O6U2U5U6 |
| 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 -2 -1 1 0 1 1],[ 2 0 1 2 1 2 1],[ 1 -1 0 2 1 1 2],[-1 -2 -2 0 0 -1 1],[ 0 -1 -1 0 0 0 0],[-1 -2 -1 1 0 0 1],[-1 -1 -2 -1 0 -1 0]] |
| Primitive based matrix | [[ 0 1 1 1 0 -1 -2],[-1 0 1 1 0 -1 -2],[-1 -1 0 1 0 -2 -2],[-1 -1 -1 0 0 -2 -1],[ 0 0 0 0 0 -1 -1],[ 1 1 2 2 1 0 -1],[ 2 2 2 1 1 1 0]] |
| If based matrix primitive | True |
| Phi of primitive based matrix | [-1,-1,-1,0,1,2,-1,-1,0,1,2,-1,0,2,2,0,2,1,1,1,1] |
| Phi over symmetry | [-2,-1,0,1,1,1,0,1,1,1,2,0,0,1,0,1,1,1,1,-1,-1] |
| Phi of -K | [-2,-1,0,1,1,1,0,1,1,1,2,0,0,1,0,1,1,1,1,-1,-1] |
| Phi of K* | [-1,-1,-1,0,1,2,-1,-1,1,0,2,-1,1,0,1,1,1,1,0,1,0] |
| Phi of -K* | [-2,-1,0,1,1,1,1,1,1,2,2,1,2,1,2,0,0,0,-1,-1,1] |
| Symmetry type of based matrix | c |
| u-polynomial | t^2-2t |
| Normalized Jones-Krushkal polynomial | 3z^2+20z+29 |
| Enhanced Jones-Krushkal polynomial | 3w^3z^2+20w^2z+29w |
| Inner characteristic polynomial | t^6+24t^4+16t^2 |
| Outer characteristic polynomial | t^7+32t^5+45t^3+4t |
| Flat arrow polynomial | -6*K1**2 - 4*K1*K2 + 2*K1 + 3*K2 + 2*K3 + 4 |
| 2-strand cable arrow polynomial | -64*K1**6 + 320*K1**4*K2 - 1856*K1**4 + 64*K1**3*K2*K3 - 768*K1**3*K3 + 128*K1**2*K2**3 - 2560*K1**2*K2**2 - 160*K1**2*K2*K4 + 6336*K1**2*K2 - 608*K1**2*K3**2 - 48*K1**2*K4**2 - 4372*K1**2 - 288*K1*K2**2*K3 - 160*K1*K2*K3*K4 + 4416*K1*K2*K3 + 1008*K1*K3*K4 + 96*K1*K4*K5 - 152*K2**4 - 96*K2**2*K3**2 - 48*K2**2*K4**2 + 408*K2**2*K4 - 3092*K2**2 + 144*K2*K3*K5 + 32*K2*K4*K6 - 1488*K3**2 - 406*K4**2 - 44*K5**2 - 4*K6**2 + 3260 |
| Genus of based matrix | 1 |
| Fillings of based matrix | [[{2, 6}, {1, 5}, {3, 4}], [{2, 6}, {3, 5}, {1, 4}], [{2, 6}, {4, 5}, {1, 3}], [{5, 6}, {2, 4}, {1, 3}]] |
| If K is slice | False |