| Min(phi) over symmetries of the knot is: [-1,-1,0,0,1,1,0,0,0,1,2,1,1,1,0,0,0,1,1,0,0] |
| Flat knots (up to 7 crossings) with same phi are :['6.2082'] |
| Arrow polynomial of the knot is: 4*K1**3 - 8*K1*K2 + K1 + 3*K3 + 1 |
| Flat knots (up to 7 crossings) with same arrow polynomial are :['6.1231', '6.1372', '6.1722', '6.1817', '6.1862', '6.2082'] |
| Outer characteristic polynomial of the knot is: t^7+14t^5+37t^3+15t |
| Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.2082'] |
| 2-strand cable arrow polynomial of the knot is: 3264*K1**4*K2 - 5824*K1**4 + 1792*K1**3*K2*K3 - 2560*K1**3*K3 - 128*K1**2*K2**4 + 448*K1**2*K2**3 + 768*K1**2*K2**2*K4 - 6176*K1**2*K2**2 - 1856*K1**2*K2*K4 + 9008*K1**2*K2 - 1600*K1**2*K3**2 - 544*K1**2*K4**2 - 3360*K1**2 + 320*K1*K2**3*K3 - 896*K1*K2**2*K3 - 448*K1*K2**2*K5 - 1024*K1*K2*K3*K4 + 7488*K1*K2*K3 + 2352*K1*K3*K4 + 768*K1*K4*K5 - 32*K2**6 + 96*K2**4*K4 - 592*K2**4 - 32*K2**3*K6 - 224*K2**2*K3**2 - 128*K2**2*K4**2 + 1544*K2**2*K4 - 3626*K2**2 + 592*K2*K3*K5 + 104*K2*K4*K6 - 1912*K3**2 - 952*K4**2 - 248*K5**2 - 22*K6**2 + 3638 |
| Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.2082'] |
| Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.20145', 'vk6.20167', 'vk6.21435', 'vk6.21452', 'vk6.27261', 'vk6.27291', 'vk6.28921', 'vk6.28951', 'vk6.38684', 'vk6.38724', 'vk6.40902', 'vk6.47268', 'vk6.47289', 'vk6.56970', 'vk6.57009', 'vk6.58122', 'vk6.62669', 'vk6.67472', 'vk6.70033', 'vk6.70053'] |
| The R3 orbit of minmal crossing diagrams contains: |
| The diagrammatic symmetry type of this knot is +. |
| The reverse -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 | O1O2U1U3O4O5U6U2O6O3U5U4 |
| R3 orbit | {'O1O2U1U3O4O5U6U2O6O3U5U4'} |
| R3 orbit length | 1 |
| Gauss code of -K | O1O2U3U2O4O5U1U6O3O6U5U4 |
| Gauss code of K* | Same |
| Gauss code of -K* | O1O2U3U2O4O5U1U6O3O6U5U4 |
| Diagrammatic symmetry type | + |
| Flat genus of the diagram | 3 |
| If K is checkerboard colorable | False |
| If K is almost classical | False |
| Based matrix from Gauss code | [[ 0 -1 1 1 0 0 -1],[ 1 0 1 0 1 1 0],[-1 -1 0 0 0 -1 -1],[-1 0 0 0 -1 0 -2],[ 0 -1 0 1 0 0 0],[ 0 -1 1 0 0 0 0],[ 1 0 1 2 0 0 0]] |
| Primitive based matrix | [[ 0 1 1 0 0 -1 -1],[-1 0 0 0 -1 0 -2],[-1 0 0 -1 0 -1 -1],[ 0 0 1 0 0 -1 0],[ 0 1 0 0 0 -1 0],[ 1 0 1 1 1 0 0],[ 1 2 1 0 0 0 0]] |
| If based matrix primitive | True |
| Phi of primitive based matrix | [-1,-1,0,0,1,1,0,0,1,0,2,1,0,1,1,0,1,0,1,0,0] |
| Phi over symmetry | [-1,-1,0,0,1,1,0,0,0,1,2,1,1,1,0,0,0,1,1,0,0] |
| Phi of -K | [-1,-1,0,0,1,1,0,0,0,1,2,1,1,1,0,0,0,1,1,0,0] |
| Phi of K* | [-1,-1,0,0,1,1,0,0,1,0,2,1,0,1,1,0,1,0,1,0,0] |
| Phi of -K* | [-1,-1,0,0,1,1,0,0,0,1,2,1,1,1,0,0,0,1,1,0,0] |
| Symmetry type of based matrix | + |
| u-polynomial | 0 |
| Normalized Jones-Krushkal polynomial | 7z^2+27z+27 |
| Enhanced Jones-Krushkal polynomial | 7w^3z^2+27w^2z+27w |
| Inner characteristic polynomial | t^6+10t^4+23t^2+9 |
| Outer characteristic polynomial | t^7+14t^5+37t^3+15t |
| Flat arrow polynomial | 4*K1**3 - 8*K1*K2 + K1 + 3*K3 + 1 |
| 2-strand cable arrow polynomial | 3264*K1**4*K2 - 5824*K1**4 + 1792*K1**3*K2*K3 - 2560*K1**3*K3 - 128*K1**2*K2**4 + 448*K1**2*K2**3 + 768*K1**2*K2**2*K4 - 6176*K1**2*K2**2 - 1856*K1**2*K2*K4 + 9008*K1**2*K2 - 1600*K1**2*K3**2 - 544*K1**2*K4**2 - 3360*K1**2 + 320*K1*K2**3*K3 - 896*K1*K2**2*K3 - 448*K1*K2**2*K5 - 1024*K1*K2*K3*K4 + 7488*K1*K2*K3 + 2352*K1*K3*K4 + 768*K1*K4*K5 - 32*K2**6 + 96*K2**4*K4 - 592*K2**4 - 32*K2**3*K6 - 224*K2**2*K3**2 - 128*K2**2*K4**2 + 1544*K2**2*K4 - 3626*K2**2 + 592*K2*K3*K5 + 104*K2*K4*K6 - 1912*K3**2 - 952*K4**2 - 248*K5**2 - 22*K6**2 + 3638 |
| Genus of based matrix | 1 |
| Fillings of based matrix | [[{1, 6}, {2, 5}, {3, 4}], [{1, 6}, {3, 5}, {2, 4}], [{1, 6}, {4, 5}, {2, 3}], [{1, 6}, {4, 5}, {3}, {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}, {5}, {4}, {1, 3}], [{3, 6}, {1, 5}, {2, 4}], [{3, 6}, {2, 5}, {1, 4}], [{3, 6}, {4, 5}, {1, 2}], [{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}, {2, 5}, {1, 3}], [{4, 6}, {3, 5}, {1, 2}], [{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}, {3, 4}, {1, 2}], [{5, 6}, {3, 4}, {2}, {1}], [{5, 6}, {4}, {1, 3}, {2}], [{6}, {2, 5}, {4}, {1, 3}], [{6}, {3, 5}, {1, 4}, {2}], [{6}, {5}, {3, 4}, {1, 2}]] |
| If K is slice | False |