| Min(phi) over symmetries of the knot is: [-2,-1,0,1,1,1,0,2,2,2,2,1,1,1,1,0,1,1,1,1,0] |
| Flat knots (up to 7 crossings) with same phi are :['6.1224'] |
| 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+17t^3 |
| Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.1224'] |
| 2-strand cable arrow polynomial of the knot is: -448*K1**6 - 256*K1**4*K2**2 + 768*K1**4*K2 - 1120*K1**4 + 224*K1**3*K2*K3 - 944*K1**2*K2**2 + 1496*K1**2*K2 - 288*K1**2*K3**2 - 112*K1**2*K4**2 - 352*K1**2 + 992*K1*K2*K3 + 336*K1*K3*K4 + 88*K1*K4*K5 - 104*K2**4 - 96*K2**2*K3**2 - 48*K2**2*K4**2 + 136*K2**2*K4 - 620*K2**2 + 72*K2*K3*K5 + 32*K2*K4*K6 - 332*K3**2 - 130*K4**2 - 28*K5**2 - 4*K6**2 + 736 |
| Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.1224'] |
| Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.11262', 'vk6.11340', 'vk6.12523', 'vk6.12634', 'vk6.17051', 'vk6.17292', 'vk6.17627', 'vk6.18918', 'vk6.18994', 'vk6.19352', 'vk6.19647', 'vk6.22261', 'vk6.24091', 'vk6.24183', 'vk6.25514', 'vk6.26128', 'vk6.26548', 'vk6.28317', 'vk6.30944', 'vk6.31067', 'vk6.31240', 'vk6.31589', 'vk6.32120', 'vk6.32239', 'vk6.32809', 'vk6.35566', 'vk6.36015', 'vk6.36424', 'vk6.37647', 'vk6.39941', 'vk6.40113', 'vk6.43525', 'vk6.44781', 'vk6.46485', 'vk6.52028', 'vk6.53393', 'vk6.55458', 'vk6.56652', 'vk6.65392', 'vk6.66107'] |
| 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 | O1O2O3O4U3U1U5O6O5U4U2U6 |
| R3 orbit | {'O1O2O3U2O4U1U5O6O5U3U4U6', 'O1O2O3O4U3U1U5O6O5U4U2U6'} |
| R3 orbit length | 2 |
| Gauss code of -K | O1O2O3O4U5U3U1O6O5U6U4U2 |
| Gauss code of K* | O1O2O3U4U3O5O6O4U2U6U1U5 |
| Gauss code of -K* | O1O2O3U4U1O4O5O6U3U6U2U5 |
| Diagrammatic symmetry type | c |
| Flat genus of the diagram | 2 |
| If K is checkerboard colorable | False |
| If K is almost classical | False |
| Based matrix from Gauss code | [[ 0 -2 0 -1 1 1 1],[ 2 0 2 0 2 2 2],[ 0 -2 0 -1 1 0 1],[ 1 0 1 0 1 1 1],[-1 -2 -1 -1 0 -1 0],[-1 -2 0 -1 1 0 1],[-1 -2 -1 -1 0 -1 0]] |
| Primitive based matrix | [[ 0 1 1 1 0 -1 -2],[-1 0 1 1 0 -1 -2],[-1 -1 0 0 -1 -1 -2],[-1 -1 0 0 -1 -1 -2],[ 0 0 1 1 0 -1 -2],[ 1 1 1 1 1 0 0],[ 2 2 2 2 2 0 0]] |
| If based matrix primitive | True |
| Phi of primitive based matrix | [-1,-1,-1,0,1,2,-1,-1,0,1,2,0,1,1,2,1,1,2,1,2,0] |
| Phi over symmetry | [-2,-1,0,1,1,1,0,2,2,2,2,1,1,1,1,0,1,1,1,1,0] |
| Phi of -K | [-2,-1,0,1,1,1,1,0,1,1,1,0,1,1,1,0,0,1,0,1,1] |
| Phi of K* | [-1,-1,-1,0,1,2,-1,0,0,1,1,1,1,1,1,0,1,1,0,0,1] |
| Phi of -K* | [-2,-1,0,1,1,1,0,2,2,2,2,1,1,1,1,0,1,1,1,1,0] |
| Symmetry type of based matrix | c |
| u-polynomial | t^2-2t |
| Normalized Jones-Krushkal polynomial | 9z+19 |
| Enhanced Jones-Krushkal polynomial | 9w^2z+19w |
| Inner characteristic polynomial | t^6+24t^4 |
| Outer characteristic polynomial | t^7+32t^5+17t^3 |
| Flat arrow polynomial | -6*K1**2 - 4*K1*K2 + 2*K1 + 3*K2 + 2*K3 + 4 |
| 2-strand cable arrow polynomial | -448*K1**6 - 256*K1**4*K2**2 + 768*K1**4*K2 - 1120*K1**4 + 224*K1**3*K2*K3 - 944*K1**2*K2**2 + 1496*K1**2*K2 - 288*K1**2*K3**2 - 112*K1**2*K4**2 - 352*K1**2 + 992*K1*K2*K3 + 336*K1*K3*K4 + 88*K1*K4*K5 - 104*K2**4 - 96*K2**2*K3**2 - 48*K2**2*K4**2 + 136*K2**2*K4 - 620*K2**2 + 72*K2*K3*K5 + 32*K2*K4*K6 - 332*K3**2 - 130*K4**2 - 28*K5**2 - 4*K6**2 + 736 |
| Genus of based matrix | 1 |
| Fillings of based matrix | [[{1, 6}, {4, 5}, {2, 3}], [{5, 6}, {1, 4}, {2, 3}]] |
| If K is slice | False |