| Min(phi) over symmetries of the knot is: [-3,0,0,0,1,2,1,1,2,1,4,-1,0,0,0,0,0,1,1,1,0] |
| Flat knots (up to 7 crossings) with same phi are :['6.1184'] |
| Arrow polynomial of the knot is: 12*K1**3 - 10*K1**2 - 10*K1*K2 - 4*K1 + 5*K2 + 2*K3 + 6 |
| Flat knots (up to 7 crossings) with same arrow polynomial are :['6.318', '6.1178', '6.1184'] |
| Outer characteristic polynomial of the knot is: t^7+43t^5+63t^3+6t |
| Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.1184'] |
| 2-strand cable arrow polynomial of the knot is: -192*K1**4*K2**2 + 768*K1**4*K2 - 1760*K1**4 + 224*K1**3*K2*K3 - 256*K1**3*K3 + 768*K1**2*K2**3 - 5584*K1**2*K2**2 - 608*K1**2*K2*K4 + 8408*K1**2*K2 - 128*K1**2*K3**2 - 6180*K1**2 + 416*K1*K2**3*K3 + 192*K1*K2**2*K3*K4 - 1568*K1*K2**2*K3 - 128*K1*K2**2*K5 - 288*K1*K2*K3*K4 - 32*K1*K2*K3*K6 + 7384*K1*K2*K3 + 1176*K1*K3*K4 + 72*K1*K4*K5 - 96*K2**6 + 224*K2**4*K4 - 1784*K2**4 - 32*K2**3*K6 - 832*K2**2*K3**2 - 552*K2**2*K4**2 + 3160*K2**2*K4 - 5284*K2**2 - 32*K2*K3**2*K4 + 640*K2*K3*K5 + 288*K2*K4*K6 + 48*K3**2*K6 - 2396*K3**2 - 1194*K4**2 - 112*K5**2 - 52*K6**2 + 5320 |
| Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.1184'] |
| Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.11298', 'vk6.11376', 'vk6.12561', 'vk6.12672', 'vk6.18354', 'vk6.18692', 'vk6.24800', 'vk6.25257', 'vk6.30975', 'vk6.31101', 'vk6.32158', 'vk6.32277', 'vk6.36978', 'vk6.37432', 'vk6.44164', 'vk6.44484', 'vk6.52054', 'vk6.52137', 'vk6.52895', 'vk6.52958', 'vk6.56128', 'vk6.56352', 'vk6.60649', 'vk6.60990', 'vk6.63665', 'vk6.63710', 'vk6.64095', 'vk6.64140', 'vk6.65778', 'vk6.66037', 'vk6.68783', 'vk6.68991'] |
| 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 | O1O2O3O4U1U5U4O6O5U3U6U2 |
| R3 orbit | {'O1O2O3O4U1U5U4O6O5U3U6U2'} |
| R3 orbit length | 1 |
| Gauss code of -K | O1O2O3O4U3U5U2O6O5U1U6U4 |
| Gauss code of K* | O1O2O3U4U2O5O4O6U1U6U5U3 |
| Gauss code of -K* | O1O2O3U4U2O5O4O6U5U3U1U6 |
| 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 1 0 2 0 0],[ 3 0 3 2 1 2 1],[-1 -3 0 -1 1 -1 0],[ 0 -2 1 0 1 -1 0],[-2 -1 -1 -1 0 -2 -1],[ 0 -2 1 1 2 0 0],[ 0 -1 0 0 1 0 0]] |
| Primitive based matrix | [[ 0 2 1 0 0 0 -3],[-2 0 -1 -1 -1 -2 -1],[-1 1 0 0 -1 -1 -3],[ 0 1 0 0 0 0 -1],[ 0 1 1 0 0 -1 -2],[ 0 2 1 0 1 0 -2],[ 3 1 3 1 2 2 0]] |
| If based matrix primitive | True |
| Phi of primitive based matrix | [-2,-1,0,0,0,3,1,1,1,2,1,0,1,1,3,0,0,1,1,2,2] |
| Phi over symmetry | [-3,0,0,0,1,2,1,1,2,1,4,-1,0,0,0,0,0,1,1,1,0] |
| Phi of -K | [-3,0,0,0,1,2,1,1,2,1,4,-1,0,0,0,0,0,1,1,1,0] |
| Phi of K* | [-2,-1,0,0,0,3,0,0,1,1,4,0,0,1,1,1,0,1,0,1,2] |
| Phi of -K* | [-3,0,0,0,1,2,1,2,2,3,1,0,0,0,1,-1,1,1,1,2,1] |
| Symmetry type of based matrix | c |
| u-polynomial | t^3-t^2-t |
| Normalized Jones-Krushkal polynomial | 4z^2+23z+31 |
| Enhanced Jones-Krushkal polynomial | 4w^3z^2+23w^2z+31w |
| Inner characteristic polynomial | t^6+29t^4+34t^2+1 |
| Outer characteristic polynomial | t^7+43t^5+63t^3+6t |
| Flat arrow polynomial | 12*K1**3 - 10*K1**2 - 10*K1*K2 - 4*K1 + 5*K2 + 2*K3 + 6 |
| 2-strand cable arrow polynomial | -192*K1**4*K2**2 + 768*K1**4*K2 - 1760*K1**4 + 224*K1**3*K2*K3 - 256*K1**3*K3 + 768*K1**2*K2**3 - 5584*K1**2*K2**2 - 608*K1**2*K2*K4 + 8408*K1**2*K2 - 128*K1**2*K3**2 - 6180*K1**2 + 416*K1*K2**3*K3 + 192*K1*K2**2*K3*K4 - 1568*K1*K2**2*K3 - 128*K1*K2**2*K5 - 288*K1*K2*K3*K4 - 32*K1*K2*K3*K6 + 7384*K1*K2*K3 + 1176*K1*K3*K4 + 72*K1*K4*K5 - 96*K2**6 + 224*K2**4*K4 - 1784*K2**4 - 32*K2**3*K6 - 832*K2**2*K3**2 - 552*K2**2*K4**2 + 3160*K2**2*K4 - 5284*K2**2 - 32*K2*K3**2*K4 + 640*K2*K3*K5 + 288*K2*K4*K6 + 48*K3**2*K6 - 2396*K3**2 - 1194*K4**2 - 112*K5**2 - 52*K6**2 + 5320 |
| 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}], [{2, 6}, {5}, {4}, {3}, {1}], [{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}, {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}, {2, 4}, {3}, {1}], [{6}, {5}, {3, 4}, {1, 2}], [{6}, {5}, {4}, {3}, {1, 2}]] |
| If K is slice | False |