| Min(phi) over symmetries of the knot is: [-3,-2,0,1,2,2,0,3,2,2,3,2,1,1,2,0,2,2,1,1,-1] |
| Flat knots (up to 7 crossings) with same phi are :['6.536'] |
| Arrow polynomial of the knot is: 4*K1**3 - 6*K1**2 - 6*K1*K2 + 3*K2 + 2*K3 + 4 |
| Flat knots (up to 7 crossings) with same arrow polynomial are :['6.311', '6.528', '6.536', '6.817', '6.982', '6.984', '6.1284'] |
| Outer characteristic polynomial of the knot is: t^7+69t^5+43t^3+3t |
| Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.536'] |
| 2-strand cable arrow polynomial of the knot is: -800*K1**4 + 32*K1**3*K2*K3 - 160*K1**3*K3 + 128*K1**2*K2**3 - 1632*K1**2*K2**2 + 32*K1**2*K2*K3**2 - 256*K1**2*K2*K4 + 3656*K1**2*K2 - 192*K1**2*K3**2 - 64*K1**2*K4**2 - 3092*K1**2 + 128*K1*K2**3*K3 - 384*K1*K2**2*K3 - 128*K1*K2**2*K5 - 64*K1*K2*K3*K4 + 3136*K1*K2*K3 + 808*K1*K3*K4 + 112*K1*K4*K5 + 24*K1*K5*K6 - 32*K2**6 + 64*K2**4*K4 - 312*K2**4 - 32*K2**3*K6 - 208*K2**2*K3**2 - 24*K2**2*K4**2 + 648*K2**2*K4 - 2332*K2**2 + 272*K2*K3*K5 + 48*K2*K4*K6 - 1240*K3**2 - 470*K4**2 - 108*K5**2 - 28*K6**2 + 2468 |
| Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.536'] |
| Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.71366', 'vk6.71425', 'vk6.71892', 'vk6.71951', 'vk6.72450', 'vk6.72609', 'vk6.72728', 'vk6.72809', 'vk6.72872', 'vk6.73041', 'vk6.73345', 'vk6.73507', 'vk6.74265', 'vk6.74387', 'vk6.74432', 'vk6.75046', 'vk6.75517', 'vk6.75829', 'vk6.76442', 'vk6.76617', 'vk6.77023', 'vk6.77752', 'vk6.77803', 'vk6.78235', 'vk6.78481', 'vk6.78630', 'vk6.78825', 'vk6.79309', 'vk6.79425', 'vk6.79843', 'vk6.79881', 'vk6.80260', 'vk6.80774', 'vk6.80871', 'vk6.85165', 'vk6.86533', 'vk6.87201', 'vk6.87340', 'vk6.89255', 'vk6.89445'] |
| 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 | O1O2O3O4O5U3U1U4O6U5U2U6 |
| R3 orbit | {'O1O2O3O4O5U3U1U4O6U5U2U6', 'O1O2O3O4U2O5U1U4O6U3U5U6'} |
| R3 orbit length | 2 |
| Gauss code of -K | O1O2O3O4O5U6U4U1O6U2U5U3 |
| Gauss code of K* | O1O2O3U4O5O6O4U2U6U1U3U5 |
| Gauss code of -K* | O1O2O3U1O4O5O6U3U4U6U2U5 |
| 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 -2 1 2 2],[ 3 0 3 0 2 3 2],[ 0 -3 0 -2 0 2 2],[ 2 0 2 0 1 2 1],[-1 -2 0 -1 0 1 1],[-2 -3 -2 -2 -1 0 1],[-2 -2 -2 -1 -1 -1 0]] |
| Primitive based matrix | [[ 0 2 2 1 0 -2 -3],[-2 0 1 -1 -2 -2 -3],[-2 -1 0 -1 -2 -1 -2],[-1 1 1 0 0 -1 -2],[ 0 2 2 0 0 -2 -3],[ 2 2 1 1 2 0 0],[ 3 3 2 2 3 0 0]] |
| If based matrix primitive | True |
| Phi of primitive based matrix | [-2,-2,-1,0,2,3,-1,1,2,2,3,1,2,1,2,0,1,2,2,3,0] |
| Phi over symmetry | [-3,-2,0,1,2,2,0,3,2,2,3,2,1,1,2,0,2,2,1,1,-1] |
| Phi of -K | [-3,-2,0,1,2,2,1,0,2,2,3,0,2,2,3,1,0,0,0,0,-1] |
| Phi of K* | [-2,-2,-1,0,2,3,-1,0,0,3,3,0,0,2,2,1,2,2,0,0,1] |
| Phi of -K* | [-3,-2,0,1,2,2,0,3,2,2,3,2,1,1,2,0,2,2,1,1,-1] |
| Symmetry type of based matrix | c |
| u-polynomial | t^3-t^2-t |
| Normalized Jones-Krushkal polynomial | z^2+14z+25 |
| Enhanced Jones-Krushkal polynomial | w^3z^2+14w^2z+25w |
| Inner characteristic polynomial | t^6+47t^4+8t^2 |
| Outer characteristic polynomial | t^7+69t^5+43t^3+3t |
| Flat arrow polynomial | 4*K1**3 - 6*K1**2 - 6*K1*K2 + 3*K2 + 2*K3 + 4 |
| 2-strand cable arrow polynomial | -800*K1**4 + 32*K1**3*K2*K3 - 160*K1**3*K3 + 128*K1**2*K2**3 - 1632*K1**2*K2**2 + 32*K1**2*K2*K3**2 - 256*K1**2*K2*K4 + 3656*K1**2*K2 - 192*K1**2*K3**2 - 64*K1**2*K4**2 - 3092*K1**2 + 128*K1*K2**3*K3 - 384*K1*K2**2*K3 - 128*K1*K2**2*K5 - 64*K1*K2*K3*K4 + 3136*K1*K2*K3 + 808*K1*K3*K4 + 112*K1*K4*K5 + 24*K1*K5*K6 - 32*K2**6 + 64*K2**4*K4 - 312*K2**4 - 32*K2**3*K6 - 208*K2**2*K3**2 - 24*K2**2*K4**2 + 648*K2**2*K4 - 2332*K2**2 + 272*K2*K3*K5 + 48*K2*K4*K6 - 1240*K3**2 - 470*K4**2 - 108*K5**2 - 28*K6**2 + 2468 |
| Genus of based matrix | 2 |
| Fillings of based matrix | [[{1, 6}, {2, 5}, {3, 4}], [{1, 6}, {2, 5}, {4}, {3}], [{1, 6}, {3, 5}, {2, 4}], [{1, 6}, {3, 5}, {4}, {2}], [{1, 6}, {4, 5}, {2, 3}], [{1, 6}, {4, 5}, {3}, {2}], [{1, 6}, {5}, {2, 4}, {3}], [{1, 6}, {5}, {3, 4}, {2}], [{1, 6}, {5}, {4}, {2, 3}], [{1, 6}, {5}, {4}, {3}, {2}], [{2, 6}, {1, 5}, {3, 4}], [{2, 6}, {1, 5}, {4}, {3}], [{2, 6}, {3, 5}, {1, 4}], [{2, 6}, {3, 5}, {4}, {1}], [{2, 6}, {4, 5}, {1, 3}], [{2, 6}, {4, 5}, {3}, {1}], [{2, 6}, {5}, {1, 4}, {3}], [{2, 6}, {5}, {3, 4}, {1}], [{2, 6}, {5}, {4}, {1, 3}], [{3, 6}, {1, 5}, {2, 4}], [{3, 6}, {1, 5}, {4}, {2}], [{3, 6}, {2, 5}, {1, 4}], [{3, 6}, {2, 5}, {4}, {1}], [{3, 6}, {4, 5}, {1, 2}], [{3, 6}, {4, 5}, {2}, {1}], [{3, 6}, {5}, {1, 4}, {2}], [{3, 6}, {5}, {2, 4}, {1}], [{3, 6}, {5}, {4}, {1, 2}], [{4, 6}, {1, 5}, {2, 3}], [{4, 6}, {1, 5}, {3}, {2}], [{4, 6}, {2, 5}, {1, 3}], [{4, 6}, {2, 5}, {3}, {1}], [{4, 6}, {3, 5}, {1, 2}], [{4, 6}, {3, 5}, {2}, {1}], [{4, 6}, {5}, {1, 3}, {2}], [{4, 6}, {5}, {2, 3}, {1}], [{4, 6}, {5}, {3}, {1, 2}], [{4, 6}, {5}, {3}, {2}, {1}], [{5, 6}, {1, 4}, {2, 3}], [{5, 6}, {1, 4}, {3}, {2}], [{5, 6}, {2, 4}, {1, 3}], [{5, 6}, {2, 4}, {3}, {1}], [{5, 6}, {3, 4}, {1, 2}], [{5, 6}, {3, 4}, {2}, {1}], [{5, 6}, {4}, {1, 3}, {2}], [{5, 6}, {4}, {2, 3}, {1}], [{5, 6}, {4}, {3}, {1, 2}], [{6}, {1, 5}, {2, 4}, {3}], [{6}, {1, 5}, {3, 4}, {2}], [{6}, {1, 5}, {4}, {2, 3}], [{6}, {2, 5}, {1, 4}, {3}], [{6}, {2, 5}, {3, 4}, {1}], [{6}, {2, 5}, {4}, {1, 3}], [{6}, {3, 5}, {1, 4}, {2}], [{6}, {3, 5}, {2, 4}, {1}], [{6}, {3, 5}, {4}, {1, 2}], [{6}, {3, 5}, {4}, {2}, {1}], [{6}, {4, 5}, {1, 3}, {2}], [{6}, {4, 5}, {2, 3}, {1}], [{6}, {4, 5}, {3}, {1, 2}], [{6}, {5}, {1, 4}, {2, 3}], [{6}, {5}, {1, 4}, {3}, {2}], [{6}, {5}, {2, 4}, {1, 3}], [{6}, {5}, {3, 4}, {1, 2}]] |
| If K is slice | False |