| Min(phi) over symmetries of the knot is: [-2,-1,0,1,1,1,0,1,1,1,2,1,0,1,1,1,1,2,-1,-1,0] |
| Flat knots (up to 7 crossings) with same phi are :['6.1534'] |
| Arrow polynomial of the knot is: -10*K1**2 - 4*K1*K2 + 2*K1 + 5*K2 + 2*K3 + 6 |
| Flat knots (up to 7 crossings) with same arrow polynomial are :['6.425', '6.655', '6.755', '6.769', '6.792', '6.1240', '6.1494', '6.1522', '6.1534', '6.1587', '6.1707', '6.1746', '6.1747', '6.1786', '6.1814', '6.1828', '6.1835', '6.1854', '6.1870'] |
| Outer characteristic polynomial of the knot is: t^7+26t^5+33t^3+7t |
| Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.1534'] |
| 2-strand cable arrow polynomial of the knot is: -320*K1**6 - 192*K1**4*K2**2 + 832*K1**4*K2 - 4000*K1**4 + 128*K1**3*K2*K3 - 192*K1**3*K3 + 288*K1**2*K2**3 - 5216*K1**2*K2**2 + 64*K1**2*K2*K3**2 - 160*K1**2*K2*K4 + 8672*K1**2*K2 - 1536*K1**2*K3**2 - 112*K1**2*K4**2 - 4212*K1**2 - 704*K1*K2**2*K3 - 128*K1*K2*K3*K4 + 7088*K1*K2*K3 + 1888*K1*K3*K4 + 112*K1*K4*K5 - 552*K2**4 - 288*K2**2*K3**2 - 48*K2**2*K4**2 + 928*K2**2*K4 - 4036*K2**2 + 272*K2*K3*K5 + 32*K2*K4*K6 - 2216*K3**2 - 686*K4**2 - 68*K5**2 - 4*K6**2 + 4364 |
| Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.1534'] |
| Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.4077', 'vk6.4110', 'vk6.5315', 'vk6.5348', 'vk6.7441', 'vk6.7470', 'vk6.8938', 'vk6.8971', 'vk6.10123', 'vk6.10288', 'vk6.10313', 'vk6.14539', 'vk6.15271', 'vk6.15398', 'vk6.15757', 'vk6.16174', 'vk6.29871', 'vk6.29904', 'vk6.33905', 'vk6.33988', 'vk6.34206', 'vk6.34373', 'vk6.48474', 'vk6.49178', 'vk6.50221', 'vk6.50252', 'vk6.51599', 'vk6.53964', 'vk6.54027', 'vk6.54177', 'vk6.54469', 'vk6.63318'] |
| 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 | O1O2O3U2O4U5U4O6O5U1U3U6 |
| R3 orbit | {'O1O2O3U2O4U5U4O6O5U1U3U6'} |
| R3 orbit length | 1 |
| Gauss code of -K | O1O2O3U4U1U3O5O4U6U5O6U2 |
| Gauss code of K* | O1O2O3U1U4U2O4U5O6O5U3U6 |
| Gauss code of -K* | O1O2O3U4U1O5O4U5O6U2U6U3 |
| 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 1 1 0 1],[ 2 0 0 2 1 1 1],[ 1 0 0 1 0 1 1],[-1 -2 -1 0 1 -2 0],[-1 -1 0 -1 0 -1 -1],[ 0 -1 -1 2 1 0 1],[-1 -1 -1 0 1 -1 0]] |
| Primitive based matrix | [[ 0 1 1 1 0 -1 -2],[-1 0 1 0 -1 -1 -1],[-1 -1 0 -1 -1 0 -1],[-1 0 1 0 -2 -1 -2],[ 0 1 1 2 0 -1 -1],[ 1 1 0 1 1 0 0],[ 2 1 1 2 1 0 0]] |
| If based matrix primitive | True |
| Phi of primitive based matrix | [-1,-1,-1,0,1,2,-1,0,1,1,1,1,1,0,1,2,1,2,1,1,0] |
| Phi over symmetry | [-2,-1,0,1,1,1,0,1,1,1,2,1,0,1,1,1,1,2,-1,-1,0] |
| Phi of -K | [-2,-1,0,1,1,1,1,1,1,2,2,0,1,1,2,-1,0,0,0,-1,-1] |
| Phi of K* | [-1,-1,-1,0,1,2,-1,-1,0,2,2,0,-1,1,1,0,1,2,0,1,1] |
| Phi of -K* | [-2,-1,0,1,1,1,0,1,1,1,2,1,0,1,1,1,1,2,-1,-1,0] |
| Symmetry type of based matrix | c |
| u-polynomial | t^2-2t |
| Normalized Jones-Krushkal polynomial | 3z^2+24z+37 |
| Enhanced Jones-Krushkal polynomial | 3w^3z^2+24w^2z+37w |
| Inner characteristic polynomial | t^6+18t^4+10t^2+1 |
| Outer characteristic polynomial | t^7+26t^5+33t^3+7t |
| Flat arrow polynomial | -10*K1**2 - 4*K1*K2 + 2*K1 + 5*K2 + 2*K3 + 6 |
| 2-strand cable arrow polynomial | -320*K1**6 - 192*K1**4*K2**2 + 832*K1**4*K2 - 4000*K1**4 + 128*K1**3*K2*K3 - 192*K1**3*K3 + 288*K1**2*K2**3 - 5216*K1**2*K2**2 + 64*K1**2*K2*K3**2 - 160*K1**2*K2*K4 + 8672*K1**2*K2 - 1536*K1**2*K3**2 - 112*K1**2*K4**2 - 4212*K1**2 - 704*K1*K2**2*K3 - 128*K1*K2*K3*K4 + 7088*K1*K2*K3 + 1888*K1*K3*K4 + 112*K1*K4*K5 - 552*K2**4 - 288*K2**2*K3**2 - 48*K2**2*K4**2 + 928*K2**2*K4 - 4036*K2**2 + 272*K2*K3*K5 + 32*K2*K4*K6 - 2216*K3**2 - 686*K4**2 - 68*K5**2 - 4*K6**2 + 4364 |
| 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}], [{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}, {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}, {3, 5}, {4}, {2}, {1}], [{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}, {2, 4}, {1, 3}], [{6}, {5}, {3, 4}, {1, 2}], [{6}, {5}, {4}, {1, 3}, {2}]] |
| If K is slice | False |