| Min(phi) over symmetries of the knot is: [-3,-1,0,1,1,2,0,1,3,3,2,0,1,1,1,0,0,0,-1,1,2] |
| Flat knots (up to 7 crossings) with same phi are :['6.1033'] |
| Arrow polynomial of the knot is: -10*K1**2 - 2*K1*K2 + K1 + 5*K2 + K3 + 6 |
| Flat knots (up to 7 crossings) with same arrow polynomial are :['6.574', '6.593', '6.604', '6.649', '6.650', '6.673', '6.690', '6.783', '6.973', '6.985', '6.1033', '6.1035'] |
| Outer characteristic polynomial of the knot is: t^7+48t^5+37t^3+4t |
| Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.1033'] |
| 2-strand cable arrow polynomial of the knot is: -256*K1**6 - 512*K1**4*K2**2 + 2880*K1**4*K2 - 6080*K1**4 + 1088*K1**3*K2*K3 - 992*K1**3*K3 + 896*K1**2*K2**3 - 8688*K1**2*K2**2 - 736*K1**2*K2*K4 + 11528*K1**2*K2 - 512*K1**2*K3**2 - 160*K1**2*K4**2 - 4172*K1**2 + 96*K1*K2**3*K3 - 960*K1*K2**2*K3 - 64*K1*K2**2*K5 + 7136*K1*K2*K3 + 1008*K1*K3*K4 + 160*K1*K4*K5 - 712*K2**4 - 96*K2**2*K3**2 - 8*K2**2*K4**2 + 872*K2**2*K4 - 3998*K2**2 + 88*K2*K3*K5 + 8*K2*K4*K6 - 1596*K3**2 - 422*K4**2 - 56*K5**2 - 2*K6**2 + 4260 |
| Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.1033'] |
| Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.11051', 'vk6.11129', 'vk6.12217', 'vk6.12324', 'vk6.16421', 'vk6.19219', 'vk6.19321', 'vk6.19514', 'vk6.19614', 'vk6.22727', 'vk6.22826', 'vk6.26031', 'vk6.26089', 'vk6.26417', 'vk6.26511', 'vk6.30628', 'vk6.30723', 'vk6.31934', 'vk6.34774', 'vk6.38092', 'vk6.38121', 'vk6.42392', 'vk6.44614', 'vk6.44743', 'vk6.51844', 'vk6.52710', 'vk6.52808', 'vk6.56578', 'vk6.56631', 'vk6.64731', 'vk6.66272', 'vk6.66297'] |
| 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 | O1O2O3O4U5U1O5U3O6U2U6U4 |
| R3 orbit | {'O1O2O3O4U5U1O5U3O6U2U6U4'} |
| R3 orbit length | 1 |
| Gauss code of -K | O1O2O3O4U1U5U3O5U2O6U4U6 |
| Gauss code of K* | O1O2O3U4U1U5U3O6O4U6O5U2 |
| Gauss code of -K* | O1O2O3U2O4U5O6O5U1U4U3U6 |
| 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 0 3 -1 1],[ 2 0 1 0 2 2 1],[ 1 -1 0 0 3 1 1],[ 0 0 0 0 1 0 0],[-3 -2 -3 -1 0 -3 0],[ 1 -2 -1 0 3 0 1],[-1 -1 -1 0 0 -1 0]] |
| Primitive based matrix | [[ 0 3 1 0 -1 -1 -2],[-3 0 0 -1 -3 -3 -2],[-1 0 0 0 -1 -1 -1],[ 0 1 0 0 0 0 0],[ 1 3 1 0 0 1 -1],[ 1 3 1 0 -1 0 -2],[ 2 2 1 0 1 2 0]] |
| If based matrix primitive | True |
| Phi of primitive based matrix | [-3,-1,0,1,1,2,0,1,3,3,2,0,1,1,1,0,0,0,-1,1,2] |
| Phi over symmetry | [-3,-1,0,1,1,2,0,1,3,3,2,0,1,1,1,0,0,0,-1,1,2] |
| Phi of -K | [-2,-1,-1,0,1,3,-1,0,2,2,3,1,1,1,1,1,1,1,1,2,2] |
| Phi of K* | [-3,-1,0,1,1,2,2,2,1,1,3,1,1,1,2,1,1,2,-1,-1,0] |
| Phi of -K* | [-2,-1,-1,0,1,3,1,2,0,1,2,1,0,1,3,0,1,3,0,1,0] |
| Symmetry type of based matrix | c |
| u-polynomial | -t^3+t^2+t |
| Normalized Jones-Krushkal polynomial | 4z^2+25z+35 |
| Enhanced Jones-Krushkal polynomial | 4w^3z^2+25w^2z+35w |
| Inner characteristic polynomial | t^6+32t^4+12t^2 |
| Outer characteristic polynomial | t^7+48t^5+37t^3+4t |
| Flat arrow polynomial | -10*K1**2 - 2*K1*K2 + K1 + 5*K2 + K3 + 6 |
| 2-strand cable arrow polynomial | -256*K1**6 - 512*K1**4*K2**2 + 2880*K1**4*K2 - 6080*K1**4 + 1088*K1**3*K2*K3 - 992*K1**3*K3 + 896*K1**2*K2**3 - 8688*K1**2*K2**2 - 736*K1**2*K2*K4 + 11528*K1**2*K2 - 512*K1**2*K3**2 - 160*K1**2*K4**2 - 4172*K1**2 + 96*K1*K2**3*K3 - 960*K1*K2**2*K3 - 64*K1*K2**2*K5 + 7136*K1*K2*K3 + 1008*K1*K3*K4 + 160*K1*K4*K5 - 712*K2**4 - 96*K2**2*K3**2 - 8*K2**2*K4**2 + 872*K2**2*K4 - 3998*K2**2 + 88*K2*K3*K5 + 8*K2*K4*K6 - 1596*K3**2 - 422*K4**2 - 56*K5**2 - 2*K6**2 + 4260 |
| 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}], [{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}, {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}, {2, 4}, {1, 3}], [{6}, {5}, {3, 4}, {1, 2}], [{6}, {5}, {4}, {1, 3}, {2}]] |
| If K is slice | False |