| Min(phi) over symmetries of the knot is: [-2,-2,0,1,1,2,-1,0,2,2,2,1,2,2,1,0,1,1,0,1,1] |
| Flat knots (up to 7 crossings) with same phi are :['6.1465'] |
| Arrow polynomial of the knot is: -10*K1**2 + 5*K2 + 6 |
| Flat knots (up to 7 crossings) with same arrow polynomial are :['6.947', '6.1027', '6.1399', '6.1430', '6.1433', '6.1442', '6.1465', '6.1469', '6.1476', '6.1505', '6.1529', '6.1606', '6.1612', '6.1613', '6.1616', '6.1649', '6.1694', '6.1736', '6.1768', '6.1771', '6.1774', '6.1884', '6.1886', '6.1887', '6.1889', '6.1960', '6.1962'] |
| Outer characteristic polynomial of the knot is: t^7+41t^5+43t^3+5t |
| Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.1465'] |
| 2-strand cable arrow polynomial of the knot is: -64*K1**6 + 640*K1**4*K2 - 5632*K1**4 + 288*K1**3*K2*K3 - 768*K1**3*K3 - 3920*K1**2*K2**2 - 256*K1**2*K2*K4 + 10776*K1**2*K2 - 384*K1**2*K3**2 - 4832*K1**2 - 352*K1*K2**2*K3 + 5640*K1*K2*K3 + 576*K1*K3*K4 - 168*K2**4 + 400*K2**2*K4 - 4536*K2**2 - 1712*K3**2 - 234*K4**2 + 4536 |
| Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.1465'] |
| Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.16558', 'vk6.16649', 'vk6.18151', 'vk6.18485', 'vk6.22957', 'vk6.23076', 'vk6.24606', 'vk6.25017', 'vk6.34950', 'vk6.35069', 'vk6.36749', 'vk6.37166', 'vk6.42519', 'vk6.42628', 'vk6.44017', 'vk6.44327', 'vk6.54805', 'vk6.54887', 'vk6.55949', 'vk6.56247', 'vk6.59233', 'vk6.59309', 'vk6.60484', 'vk6.60847', 'vk6.64779', 'vk6.64842', 'vk6.65614', 'vk6.65919', 'vk6.68077', 'vk6.68140', 'vk6.68685', 'vk6.68894'] |
| 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 | O1O2O3U1O4U2O5U4U6U3O6U5 |
| R3 orbit | {'O1O2O3U1O4U2O5U4U6U3O6U5'} |
| R3 orbit length | 1 |
| Gauss code of -K | O1O2O3U4O5U1U5U6O4U2O6U3 |
| Gauss code of K* | O1O2O3U2O4U5U6U3O5U1O6U4 |
| Gauss code of -K* | O1O2O3U4O5U3O6U1U5U6O4U2 |
| 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 2 0 2 -1],[ 2 0 1 2 1 1 1],[ 1 -1 0 2 1 2 0],[-2 -2 -2 0 0 1 -2],[ 0 -1 -1 0 0 1 0],[-2 -1 -2 -1 -1 0 -2],[ 1 -1 0 2 0 2 0]] |
| Primitive based matrix | [[ 0 2 2 0 -1 -1 -2],[-2 0 1 0 -2 -2 -2],[-2 -1 0 -1 -2 -2 -1],[ 0 0 1 0 0 -1 -1],[ 1 2 2 0 0 0 -1],[ 1 2 2 1 0 0 -1],[ 2 2 1 1 1 1 0]] |
| If based matrix primitive | True |
| Phi of primitive based matrix | [-2,-2,0,1,1,2,-1,0,2,2,2,1,2,2,1,0,1,1,0,1,1] |
| Phi over symmetry | [-2,-2,0,1,1,2,-1,0,2,2,2,1,2,2,1,0,1,1,0,1,1] |
| Phi of -K | [-2,-1,-1,0,2,2,0,0,1,2,3,0,0,1,1,1,1,1,2,1,-1] |
| Phi of K* | [-2,-2,0,1,1,2,-1,1,1,1,3,2,1,1,2,0,1,1,0,0,0] |
| Phi of -K* | [-2,-1,-1,0,2,2,1,1,1,1,2,0,0,2,2,1,2,2,1,0,-1] |
| Symmetry type of based matrix | c |
| u-polynomial | -t^2+2t |
| Normalized Jones-Krushkal polynomial | 2z^2+23z+39 |
| Enhanced Jones-Krushkal polynomial | 2w^3z^2+23w^2z+39w |
| Inner characteristic polynomial | t^6+27t^4+22t^2+1 |
| Outer characteristic polynomial | t^7+41t^5+43t^3+5t |
| Flat arrow polynomial | -10*K1**2 + 5*K2 + 6 |
| 2-strand cable arrow polynomial | -64*K1**6 + 640*K1**4*K2 - 5632*K1**4 + 288*K1**3*K2*K3 - 768*K1**3*K3 - 3920*K1**2*K2**2 - 256*K1**2*K2*K4 + 10776*K1**2*K2 - 384*K1**2*K3**2 - 4832*K1**2 - 352*K1*K2**2*K3 + 5640*K1*K2*K3 + 576*K1*K3*K4 - 168*K2**4 + 400*K2**2*K4 - 4536*K2**2 - 1712*K3**2 - 234*K4**2 + 4536 |
| Genus of based matrix | 1 |
| Fillings of based matrix | [[{1, 6}, {2, 5}, {3, 4}], [{1, 6}, {3, 5}, {2, 4}]] |
| If K is slice | False |