| Min(phi) over symmetries of the knot is: [-3,-1,-1,1,2,2,0,1,1,3,3,0,1,1,1,1,2,2,-1,-1,0] |
| Flat knots (up to 7 crossings) with same phi are :['6.550'] |
| Arrow polynomial of the knot is: 4*K1**3 - 2*K1*K2 - 2*K1 + 1 |
| Flat knots (up to 7 crossings) with same arrow polynomial are :['6.233', '6.340', '6.382', '6.550', '6.656', '6.663', '6.683', '6.698', '6.739', '6.745', '6.759', '6.765', '6.1357', '6.1358', '6.1370'] |
| Outer characteristic polynomial of the knot is: t^7+62t^5+33t^3 |
| Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.550'] |
| 2-strand cable arrow polynomial of the knot is: -448*K1**2*K2**4 + 512*K1**2*K2**3 - 2384*K1**2*K2**2 + 1760*K1**2*K2 - 896*K1**2 + 384*K1*K2**3*K3 + 1296*K1*K2*K3 - 32*K2**6 + 32*K2**4*K4 - 448*K2**4 - 80*K2**2*K3**2 - 8*K2**2*K4**2 + 128*K2**2*K4 - 192*K2**2 - 144*K3**2 - 8*K4**2 + 526 |
| Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.550'] |
| Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.16785', 'vk6.16789', 'vk6.16816', 'vk6.16820', 'vk6.18167', 'vk6.18169', 'vk6.18504', 'vk6.18506', 'vk6.23201', 'vk6.23205', 'vk6.23405', 'vk6.23712', 'vk6.24625', 'vk6.25043', 'vk6.25045', 'vk6.35216', 'vk6.35913', 'vk6.36763', 'vk6.37192', 'vk6.37194', 'vk6.39383', 'vk6.41572', 'vk6.42697', 'vk6.42701', 'vk6.44343', 'vk6.44345', 'vk6.45958', 'vk6.47637', 'vk6.54976', 'vk6.55009', 'vk6.55967', 'vk6.57399', 'vk6.59366', 'vk6.59370', 'vk6.59555', 'vk6.62068', 'vk6.65183', 'vk6.65633', 'vk6.68167', 'vk6.68171'] |
| 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 | O1O2O3O4O5U3U6U1O6U4U5U2 |
| R3 orbit | {'O1O2O3O4O5U3U6U1O6U4U5U2', 'O1O2O3O4U2O5U6U1O6U4U3U5'} |
| R3 orbit length | 2 |
| Gauss code of -K | O1O2O3O4O5U4U1U2O6U5U6U3 |
| Gauss code of K* | O1O2O3U2O4O5O6U3U6U1U4U5 |
| Gauss code of -K* | O1O2O3U4O5O4O6U2U3U6U1U5 |
| Diagrammatic symmetry type | c |
| Flat genus of the diagram | 2 |
| If K is checkerboard colorable | False |
| If K is almost classical | False |
| Based matrix from Gauss code | [[ 0 -2 1 -2 1 3 -1],[ 2 0 2 0 1 2 2],[-1 -2 0 -2 0 2 -1],[ 2 0 2 0 1 2 2],[-1 -1 0 -1 0 1 -1],[-3 -2 -2 -2 -1 0 -3],[ 1 -2 1 -2 1 3 0]] |
| Primitive based matrix | [[ 0 3 1 1 -1 -2 -2],[-3 0 -1 -2 -3 -2 -2],[-1 1 0 0 -1 -1 -1],[-1 2 0 0 -1 -2 -2],[ 1 3 1 1 0 -2 -2],[ 2 2 1 2 2 0 0],[ 2 2 1 2 2 0 0]] |
| If based matrix primitive | True |
| Phi of primitive based matrix | [-3,-1,-1,1,2,2,1,2,3,2,2,0,1,1,1,1,2,2,2,2,0] |
| Phi over symmetry | [-3,-1,-1,1,2,2,0,1,1,3,3,0,1,1,1,1,2,2,-1,-1,0] |
| Phi of -K | [-2,-2,-1,1,1,3,0,-1,1,2,3,-1,1,2,3,1,1,1,0,0,1] |
| Phi of K* | [-3,-1,-1,1,2,2,0,1,1,3,3,0,1,1,1,1,2,2,-1,-1,0] |
| Phi of -K* | [-2,-2,-1,1,1,3,0,2,1,2,2,2,1,2,2,1,1,3,0,1,2] |
| Symmetry type of based matrix | c |
| u-polynomial | -t^3+2t^2-t |
| Normalized Jones-Krushkal polynomial | z+3 |
| Enhanced Jones-Krushkal polynomial | -12w^3z+13w^2z+3w |
| Inner characteristic polynomial | t^6+42t^4+5t^2 |
| Outer characteristic polynomial | t^7+62t^5+33t^3 |
| Flat arrow polynomial | 4*K1**3 - 2*K1*K2 - 2*K1 + 1 |
| 2-strand cable arrow polynomial | -448*K1**2*K2**4 + 512*K1**2*K2**3 - 2384*K1**2*K2**2 + 1760*K1**2*K2 - 896*K1**2 + 384*K1*K2**3*K3 + 1296*K1*K2*K3 - 32*K2**6 + 32*K2**4*K4 - 448*K2**4 - 80*K2**2*K3**2 - 8*K2**2*K4**2 + 128*K2**2*K4 - 192*K2**2 - 144*K3**2 - 8*K4**2 + 526 |
| 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}], [{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}], [{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}], [{5, 6}, {4}, {3}, {2}, {1}], [{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}, {2, 5}, {4}, {3}, {1}], [{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}, {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}, {2, 4}, {3}, {1}], [{6}, {5}, {3, 4}, {1, 2}], [{6}, {5}, {3, 4}, {2}, {1}], [{6}, {5}, {4}, {1, 3}, {2}], [{6}, {5}, {4}, {2, 3}, {1}], [{6}, {5}, {4}, {3}, {1, 2}], [{6}, {5}, {4}, {3}, {2}, {1}]] |
| If K is slice | False |