| Min(phi) over symmetries of the knot is: [-3,-1,0,1,1,2,1,1,2,3,1,0,2,2,2,0,0,1,0,0,1] |
| Flat knots (up to 7 crossings) with same phi are :['6.956'] |
| Arrow polynomial of the knot is: 8*K1**3 - 6*K1**2 - 6*K1*K2 - 3*K1 + 3*K2 + K3 + 4 |
| Flat knots (up to 7 crossings) with same arrow polynomial are :['6.237', '6.602', '6.956', '6.986', '6.992', '6.1052', '6.1059'] |
| Outer characteristic polynomial of the knot is: t^7+48t^5+106t^3+4t |
| Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.956'] |
| 2-strand cable arrow polynomial of the knot is: 160*K1**4*K2 - 464*K1**4 - 224*K1**3*K3 + 384*K1**2*K2**3 - 1744*K1**2*K2**2 + 64*K1**2*K2*K3**2 + 3488*K1**2*K2 - 112*K1**2*K3**2 - 2856*K1**2 + 128*K1*K2**3*K3 - 1088*K1*K2**2*K3 - 64*K1*K2**2*K5 - 128*K1*K2*K3*K4 + 3040*K1*K2*K3 + 496*K1*K3*K4 + 56*K1*K4*K5 - 64*K2**6 + 96*K2**4*K4 - 664*K2**4 - 32*K2**3*K6 - 208*K2**2*K3**2 - 40*K2**2*K4**2 + 1080*K2**2*K4 - 2210*K2**2 - 32*K2*K3**2*K4 + 216*K2*K3*K5 + 40*K2*K4*K6 + 8*K3**2*K6 - 1060*K3**2 - 374*K4**2 - 60*K5**2 - 6*K6**2 + 2172 |
| Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.956'] |
| Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.11240', 'vk6.11318', 'vk6.12505', 'vk6.12616', 'vk6.18219', 'vk6.18554', 'vk6.24682', 'vk6.25101', 'vk6.30914', 'vk6.31037', 'vk6.32102', 'vk6.32221', 'vk6.36813', 'vk6.37272', 'vk6.44054', 'vk6.44394', 'vk6.51990', 'vk6.52085', 'vk6.52871', 'vk6.52918', 'vk6.56012', 'vk6.56286', 'vk6.60552', 'vk6.60893', 'vk6.63642', 'vk6.63687', 'vk6.64074', 'vk6.64119', 'vk6.65677', 'vk6.65965', 'vk6.68723', 'vk6.68932', 'vk6.73768', 'vk6.73906', 'vk6.78707', 'vk6.78760', 'vk6.78899', 'vk6.78908', 'vk6.84466', 'vk6.88348'] |
| 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 | O1O2O3O4U5U2O6O5U1U4U6U3 |
| R3 orbit | {'O1O2O3U4O5U2O4O6U1U6U5U3', 'O1O2O3O4U5U2O6O5U1U4U6U3'} |
| R3 orbit length | 2 |
| Gauss code of -K | O1O2O3O4U2U5U1U4O6O5U3U6 |
| Gauss code of K* | O1O2O3O4U1U5U4U2O6O5U3U6 |
| Gauss code of -K* | O1O2O3O4U5U2O6O5U3U1U6U4 |
| 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 2 1 0 1],[ 3 0 1 4 2 2 1],[ 1 -1 0 1 0 1 0],[-2 -4 -1 0 -1 -1 0],[-1 -2 0 1 0 -1 0],[ 0 -2 -1 1 1 0 1],[-1 -1 0 0 0 -1 0]] |
| Primitive based matrix | [[ 0 2 1 1 0 -1 -3],[-2 0 0 -1 -1 -1 -4],[-1 0 0 0 -1 0 -1],[-1 1 0 0 -1 0 -2],[ 0 1 1 1 0 -1 -2],[ 1 1 0 0 1 0 -1],[ 3 4 1 2 2 1 0]] |
| If based matrix primitive | True |
| Phi of primitive based matrix | [-2,-1,-1,0,1,3,0,1,1,1,4,0,1,0,1,1,0,2,1,2,1] |
| Phi over symmetry | [-3,-1,0,1,1,2,1,1,2,3,1,0,2,2,2,0,0,1,0,0,1] |
| Phi of -K | [-3,-1,0,1,1,2,1,1,2,3,1,0,2,2,2,0,0,1,0,0,1] |
| Phi of K* | [-2,-1,-1,0,1,3,0,1,1,2,1,0,0,2,2,0,2,3,0,1,1] |
| Phi of -K* | [-3,-1,0,1,1,2,1,2,1,2,4,1,0,0,1,1,1,1,0,0,1] |
| Symmetry type of based matrix | c |
| u-polynomial | t^3-t^2-t |
| Normalized Jones-Krushkal polynomial | 2z^2+15z+23 |
| Enhanced Jones-Krushkal polynomial | 2w^3z^2+15w^2z+23w |
| Inner characteristic polynomial | t^6+32t^4+57t^2+1 |
| Outer characteristic polynomial | t^7+48t^5+106t^3+4t |
| Flat arrow polynomial | 8*K1**3 - 6*K1**2 - 6*K1*K2 - 3*K1 + 3*K2 + K3 + 4 |
| 2-strand cable arrow polynomial | 160*K1**4*K2 - 464*K1**4 - 224*K1**3*K3 + 384*K1**2*K2**3 - 1744*K1**2*K2**2 + 64*K1**2*K2*K3**2 + 3488*K1**2*K2 - 112*K1**2*K3**2 - 2856*K1**2 + 128*K1*K2**3*K3 - 1088*K1*K2**2*K3 - 64*K1*K2**2*K5 - 128*K1*K2*K3*K4 + 3040*K1*K2*K3 + 496*K1*K3*K4 + 56*K1*K4*K5 - 64*K2**6 + 96*K2**4*K4 - 664*K2**4 - 32*K2**3*K6 - 208*K2**2*K3**2 - 40*K2**2*K4**2 + 1080*K2**2*K4 - 2210*K2**2 - 32*K2*K3**2*K4 + 216*K2*K3*K5 + 40*K2*K4*K6 + 8*K3**2*K6 - 1060*K3**2 - 374*K4**2 - 60*K5**2 - 6*K6**2 + 2172 |
| 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}], [{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}], [{6}, {5}, {4}, {2, 3}, {1}], [{6}, {5}, {4}, {3}, {1, 2}]] |
| If K is slice | False |