| Min(phi) over symmetries of the knot is: [-3,-2,0,1,1,3,0,2,2,3,3,1,1,2,1,1,0,2,-1,0,3] |
| Flat knots (up to 7 crossings) with same phi are :['6.425'] |
| Arrow polynomial of the knot is: -10*K1**2 - 4*K1*K2 + 2*K1 + 5*K2 + 2*K3 + 6 |
| Flat knots (up to 7 crossings) with same arrow polynomial are :['6.425', '6.655', '6.755', '6.769', '6.792', '6.1240', '6.1494', '6.1522', '6.1534', '6.1587', '6.1707', '6.1746', '6.1747', '6.1786', '6.1814', '6.1828', '6.1835', '6.1854', '6.1870'] |
| Outer characteristic polynomial of the knot is: t^7+72t^5+85t^3+4t |
| Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.425', '6.428'] |
| 2-strand cable arrow polynomial of the knot is: -64*K1**6 + 160*K1**4*K2 - 1952*K1**4 + 64*K1**3*K2*K3 - 800*K1**3*K3 - 2368*K1**2*K2**2 + 256*K1**2*K2*K3**2 - 352*K1**2*K2*K4 + 6880*K1**2*K2 - 832*K1**2*K3**2 - 32*K1**2*K3*K5 - 176*K1**2*K4**2 - 5372*K1**2 - 736*K1*K2**2*K3 - 32*K1*K2**2*K5 - 160*K1*K2*K3*K4 + 6048*K1*K2*K3 - 96*K1*K2*K4*K5 + 1712*K1*K3*K4 + 256*K1*K4*K5 + 24*K1*K5*K6 - 296*K2**4 - 384*K2**2*K3**2 - 48*K2**2*K4**2 + 896*K2**2*K4 - 4140*K2**2 + 392*K2*K3*K5 + 88*K2*K4*K6 - 2288*K3**2 - 794*K4**2 - 148*K5**2 - 20*K6**2 + 4312 |
| Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.425'] |
| Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.20014', 'vk6.20060', 'vk6.21286', 'vk6.21342', 'vk6.27065', 'vk6.27125', 'vk6.28770', 'vk6.28814', 'vk6.38462', 'vk6.38526', 'vk6.40651', 'vk6.40723', 'vk6.45346', 'vk6.45426', 'vk6.47115', 'vk6.47168', 'vk6.56829', 'vk6.56881', 'vk6.57963', 'vk6.58019', 'vk6.61347', 'vk6.61411', 'vk6.62523', 'vk6.62568', 'vk6.66549', 'vk6.66589', 'vk6.67338', 'vk6.67380', 'vk6.69195', 'vk6.69241', 'vk6.69946', 'vk6.69982'] |
| 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 | O1O2O3O4O5U6U1O6U3U5U2U4 |
| R3 orbit | {'O1O2O3O4O5U6U1O6U3U5U2U4'} |
| R3 orbit length | 1 |
| Gauss code of -K | O1O2O3O4O5U2U4U1U3O6U5U6 |
| Gauss code of K* | O1O2O3O4U5U3U1U4U2O6O5U6 |
| Gauss code of -K* | O1O2O3O4U5O6O5U3U1U4U2U6 |
| 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 -3 0 -1 3 2 -1],[ 3 0 2 0 3 1 3],[ 0 -2 0 -1 2 1 0],[ 1 0 1 0 2 1 1],[-3 -3 -2 -2 0 0 -3],[-2 -1 -1 -1 0 0 -2],[ 1 -3 0 -1 3 2 0]] |
| Primitive based matrix | [[ 0 3 2 0 -1 -1 -3],[-3 0 0 -2 -2 -3 -3],[-2 0 0 -1 -1 -2 -1],[ 0 2 1 0 -1 0 -2],[ 1 2 1 1 0 1 0],[ 1 3 2 0 -1 0 -3],[ 3 3 1 2 0 3 0]] |
| If based matrix primitive | True |
| Phi of primitive based matrix | [-3,-2,0,1,1,3,0,2,2,3,3,1,1,2,1,1,0,2,-1,0,3] |
| Phi over symmetry | [-3,-2,0,1,1,3,0,2,2,3,3,1,1,2,1,1,0,2,-1,0,3] |
| Phi of -K | [-3,-1,-1,0,2,3,-1,2,1,4,3,1,1,1,1,0,2,2,1,1,1] |
| Phi of K* | [-3,-2,0,1,1,3,1,1,1,2,3,1,1,2,4,1,0,1,-1,-1,2] |
| Phi of -K* | [-3,-1,-1,0,2,3,0,3,2,1,3,1,1,1,2,0,2,3,1,2,0] |
| Symmetry type of based matrix | c |
| u-polynomial | -t^2+2t |
| Normalized Jones-Krushkal polynomial | 17z+35 |
| Enhanced Jones-Krushkal polynomial | 17w^2z+35w |
| Inner characteristic polynomial | t^6+48t^4+32t^2 |
| Outer characteristic polynomial | t^7+72t^5+85t^3+4t |
| Flat arrow polynomial | -10*K1**2 - 4*K1*K2 + 2*K1 + 5*K2 + 2*K3 + 6 |
| 2-strand cable arrow polynomial | -64*K1**6 + 160*K1**4*K2 - 1952*K1**4 + 64*K1**3*K2*K3 - 800*K1**3*K3 - 2368*K1**2*K2**2 + 256*K1**2*K2*K3**2 - 352*K1**2*K2*K4 + 6880*K1**2*K2 - 832*K1**2*K3**2 - 32*K1**2*K3*K5 - 176*K1**2*K4**2 - 5372*K1**2 - 736*K1*K2**2*K3 - 32*K1*K2**2*K5 - 160*K1*K2*K3*K4 + 6048*K1*K2*K3 - 96*K1*K2*K4*K5 + 1712*K1*K3*K4 + 256*K1*K4*K5 + 24*K1*K5*K6 - 296*K2**4 - 384*K2**2*K3**2 - 48*K2**2*K4**2 + 896*K2**2*K4 - 4140*K2**2 + 392*K2*K3*K5 + 88*K2*K4*K6 - 2288*K3**2 - 794*K4**2 - 148*K5**2 - 20*K6**2 + 4312 |
| Genus of based matrix | 1 |
| Fillings of based matrix | [[{1, 6}, {2, 5}, {3, 4}], [{1, 6}, {5}, {3, 4}, {2}], [{3, 6}, {4, 5}, {1, 2}]] |
| If K is slice | False |