| Min(phi) over symmetries of the knot is: [-3,-3,1,1,2,2,0,1,2,1,3,1,3,2,4,-1,0,-1,0,1,0] |
| Flat knots (up to 7 crossings) with same phi are :['6.440'] |
| Arrow polynomial of the knot is: 4*K1**3 - 4*K1*K2 - K1 + K3 + 1 |
| Flat knots (up to 7 crossings) with same arrow polynomial are :['6.395', '6.430', '6.440', '6.548', '6.551', '6.774', '6.832', '6.887', '6.908', '6.911', '6.1205', '6.1332', '6.1339', '6.1341', '6.1346', '6.1382', '6.1488', '6.1651', '6.1655', '6.1686'] |
| Outer characteristic polynomial of the knot is: t^7+88t^5+272t^3+4t |
| Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.440'] |
| 2-strand cable arrow polynomial of the knot is: -192*K1**2*K2**4 + 160*K1**2*K2**3 + 128*K1**2*K2**2*K4 - 2128*K1**2*K2**2 - 192*K1**2*K2*K4 + 2352*K1**2*K2 - 64*K1**2*K4**2 - 1808*K1**2 + 256*K1*K2**3*K3 - 608*K1*K2**2*K3 - 256*K1*K2**2*K5 - 64*K1*K2*K3*K6 + 2712*K1*K2*K3 + 416*K1*K3*K4 + 56*K1*K4*K5 - 32*K2**6 + 64*K2**4*K4 - 480*K2**4 - 32*K2**3*K6 - 208*K2**2*K3**2 - 80*K2**2*K4**2 + 960*K2**2*K4 - 1630*K2**2 - 32*K2*K3**2*K4 + 328*K2*K3*K5 + 112*K2*K4*K6 + 48*K3**2*K6 - 824*K3**2 - 348*K4**2 - 80*K5**2 - 34*K6**2 + 1498 |
| Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.440'] |
| Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.17002', 'vk6.17244', 'vk6.17535', 'vk6.17546', 'vk6.17590', 'vk6.17603', 'vk6.21913', 'vk6.24041', 'vk6.24056', 'vk6.24150', 'vk6.27971', 'vk6.29444', 'vk6.35478', 'vk6.35928', 'vk6.36323', 'vk6.36338', 'vk6.36404', 'vk6.39377', 'vk6.41562', 'vk6.43448', 'vk6.43459', 'vk6.43505', 'vk6.45950', 'vk6.47631', 'vk6.55183', 'vk6.55426', 'vk6.55633', 'vk6.55636', 'vk6.55661', 'vk6.58563', 'vk6.60151', 'vk6.60211', 'vk6.62054', 'vk6.63045', 'vk6.64981', 'vk6.65192', 'vk6.65342', 'vk6.65373', 'vk6.68508', 'vk6.68531'] |
| 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 | O1O2O3O4O5U6U2O6U3U1U5U4 |
| R3 orbit | {'O1O2O3O4O5U3U6U2O6U1U5U4', 'O1O2O3O4O5U6U2O6U3U1U5U4'} |
| R3 orbit length | 2 |
| Gauss code of -K | O1O2O3O4O5U2U1U5U3O6U4U6 |
| Gauss code of K* | O1O2O3O4U2U5U1U4U3O6O5U6 |
| Gauss code of -K* | O1O2O3O4U5O6O5U2U1U4U6U3 |
| 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 -2 -1 3 3 -1],[ 2 0 0 1 4 3 1],[ 2 0 0 0 2 1 2],[ 1 -1 0 0 2 1 1],[-3 -4 -2 -2 0 0 -3],[-3 -3 -1 -1 0 0 -3],[ 1 -1 -2 -1 3 3 0]] |
| Primitive based matrix | [[ 0 3 3 -1 -1 -2 -2],[-3 0 0 -1 -3 -1 -3],[-3 0 0 -2 -3 -2 -4],[ 1 1 2 0 1 0 -1],[ 1 3 3 -1 0 -2 -1],[ 2 1 2 0 2 0 0],[ 2 3 4 1 1 0 0]] |
| If based matrix primitive | True |
| Phi of primitive based matrix | [-3,-3,1,1,2,2,0,1,3,1,3,2,3,2,4,-1,0,1,2,1,0] |
| Phi over symmetry | [-3,-3,1,1,2,2,0,1,2,1,3,1,3,2,4,-1,0,-1,0,1,0] |
| Phi of -K | [-2,-2,-1,-1,3,3,0,-1,1,3,4,0,0,1,2,1,1,1,2,3,0] |
| Phi of K* | [-3,-3,1,1,2,2,0,1,2,1,3,1,3,2,4,-1,0,-1,0,1,0] |
| Phi of -K* | [-2,-2,-1,-1,3,3,0,0,2,1,2,1,1,3,4,1,1,2,3,3,0] |
| Symmetry type of based matrix | c |
| u-polynomial | -2t^3+2t^2+2t |
| Normalized Jones-Krushkal polynomial | 6z^2+19z+15 |
| Enhanced Jones-Krushkal polynomial | 6w^3z^2+19w^2z+15w |
| Inner characteristic polynomial | t^6+60t^4+160t^2+1 |
| Outer characteristic polynomial | t^7+88t^5+272t^3+4t |
| Flat arrow polynomial | 4*K1**3 - 4*K1*K2 - K1 + K3 + 1 |
| 2-strand cable arrow polynomial | -192*K1**2*K2**4 + 160*K1**2*K2**3 + 128*K1**2*K2**2*K4 - 2128*K1**2*K2**2 - 192*K1**2*K2*K4 + 2352*K1**2*K2 - 64*K1**2*K4**2 - 1808*K1**2 + 256*K1*K2**3*K3 - 608*K1*K2**2*K3 - 256*K1*K2**2*K5 - 64*K1*K2*K3*K6 + 2712*K1*K2*K3 + 416*K1*K3*K4 + 56*K1*K4*K5 - 32*K2**6 + 64*K2**4*K4 - 480*K2**4 - 32*K2**3*K6 - 208*K2**2*K3**2 - 80*K2**2*K4**2 + 960*K2**2*K4 - 1630*K2**2 - 32*K2*K3**2*K4 + 328*K2*K3*K5 + 112*K2*K4*K6 + 48*K3**2*K6 - 824*K3**2 - 348*K4**2 - 80*K5**2 - 34*K6**2 + 1498 |
| 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}], [{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}], [{3, 6}, {5}, {4}, {2}, {1}], [{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}], [{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}, {1, 5}, {4}, {3}, {2}], [{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}, {4, 5}, {1, 3}, {2}], [{6}, {4, 5}, {2, 3}, {1}], [{6}, {4, 5}, {3}, {1, 2}], [{6}, {4, 5}, {3}, {2}, {1}], [{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 |