| Min(phi) over symmetries of the knot is: [-3,-1,0,1,1,2,0,1,2,4,2,0,0,1,1,1,1,1,-1,1,2] |
| Flat knots (up to 7 crossings) with same phi are :['6.1273'] |
| Arrow polynomial of the knot is: -6*K1**2 - 2*K1*K2 + K1 + 3*K2 + K3 + 4 |
| Flat knots (up to 7 crossings) with same arrow polynomial are :['6.323', '6.380', '6.444', '6.472', '6.523', '6.579', '6.592', '6.595', '6.609', '6.614', '6.620', '6.644', '6.648', '6.669', '6.671', '6.681', '6.693', '6.724', '6.725', '6.757', '6.766', '6.785', '6.786', '6.797', '6.798', '6.816', '6.833', '6.972', '6.978', '6.1056', '6.1064', '6.1066', '6.1087', '6.1094', '6.1273', '6.1277', '6.1282', '6.1295', '6.1300', '6.1313', '6.1344', '6.1353', '6.1354'] |
| Outer characteristic polynomial of the knot is: t^7+52t^5+55t^3+5t |
| Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.1273'] |
| 2-strand cable arrow polynomial of the knot is: -192*K1**4*K2**2 + 544*K1**4*K2 - 1600*K1**4 + 224*K1**3*K2*K3 - 192*K1**3*K3 + 384*K1**2*K2**3 - 3280*K1**2*K2**2 - 32*K1**2*K2*K4 + 6280*K1**2*K2 - 224*K1**2*K3**2 - 4184*K1**2 + 96*K1*K2**3*K3 - 832*K1*K2**2*K3 + 3832*K1*K2*K3 + 368*K1*K3*K4 + 8*K1*K4*K5 - 376*K2**4 - 208*K2**2*K3**2 - 8*K2**2*K4**2 + 520*K2**2*K4 - 3006*K2**2 + 112*K2*K3*K5 + 8*K2*K4*K6 - 1084*K3**2 - 158*K4**2 - 20*K5**2 - 2*K6**2 + 3020 |
| Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.1273'] |
| Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.11237', 'vk6.11317', 'vk6.12500', 'vk6.12613', 'vk6.18212', 'vk6.18549', 'vk6.24673', 'vk6.25096', 'vk6.30917', 'vk6.31042', 'vk6.32105', 'vk6.32226', 'vk6.36806', 'vk6.37265', 'vk6.44047', 'vk6.44389', 'vk6.51985', 'vk6.52082', 'vk6.52866', 'vk6.52915', 'vk6.56017', 'vk6.56293', 'vk6.60559', 'vk6.60900', 'vk6.63645', 'vk6.63691', 'vk6.64075', 'vk6.64121', 'vk6.65682', 'vk6.65974', 'vk6.68728', 'vk6.68938'] |
| 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 | O1O2O3U1O4O5U3U4O6U2U6U5 |
| R3 orbit | {'O1O2O3U1O4O5U3U4O6U2U6U5'} |
| R3 orbit length | 1 |
| Gauss code of -K | O1O2O3U4U5U2O5U6U1O4O6U3 |
| Gauss code of K* | O1O2O3U4U1U5O4U6U3O5O6U2 |
| Gauss code of -K* | O1O2O3U2O4O5U1U4O6U5U3U6 |
| 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 0 3 1],[ 2 0 2 1 1 2 1],[ 1 -2 0 -1 1 4 1],[ 1 -1 1 0 1 2 0],[ 0 -1 -1 -1 0 1 0],[-3 -2 -4 -2 -1 0 0],[-1 -1 -1 0 0 0 0]] |
| Primitive based matrix | [[ 0 3 1 0 -1 -1 -2],[-3 0 0 -1 -2 -4 -2],[-1 0 0 0 0 -1 -1],[ 0 1 0 0 -1 -1 -1],[ 1 2 0 1 0 1 -1],[ 1 4 1 1 -1 0 -2],[ 2 2 1 1 1 2 0]] |
| If based matrix primitive | True |
| Phi of primitive based matrix | [-3,-1,0,1,1,2,0,1,2,4,2,0,0,1,1,1,1,1,-1,1,2] |
| Phi over symmetry | [-3,-1,0,1,1,2,0,1,2,4,2,0,0,1,1,1,1,1,-1,1,2] |
| Phi of -K | [-2,-1,-1,0,1,3,-1,0,1,2,3,1,0,1,0,0,2,2,1,2,2] |
| Phi of K* | [-3,-1,0,1,1,2,2,2,0,2,3,1,1,2,2,0,0,1,-1,-1,0] |
| Phi of -K* | [-2,-1,-1,0,1,3,1,2,1,1,2,1,1,0,2,1,1,4,0,1,0] |
| 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+36t^4+26t^2 |
| Outer characteristic polynomial | t^7+52t^5+55t^3+5t |
| Flat arrow polynomial | -6*K1**2 - 2*K1*K2 + K1 + 3*K2 + K3 + 4 |
| 2-strand cable arrow polynomial | -192*K1**4*K2**2 + 544*K1**4*K2 - 1600*K1**4 + 224*K1**3*K2*K3 - 192*K1**3*K3 + 384*K1**2*K2**3 - 3280*K1**2*K2**2 - 32*K1**2*K2*K4 + 6280*K1**2*K2 - 224*K1**2*K3**2 - 4184*K1**2 + 96*K1*K2**3*K3 - 832*K1*K2**2*K3 + 3832*K1*K2*K3 + 368*K1*K3*K4 + 8*K1*K4*K5 - 376*K2**4 - 208*K2**2*K3**2 - 8*K2**2*K4**2 + 520*K2**2*K4 - 3006*K2**2 + 112*K2*K3*K5 + 8*K2*K4*K6 - 1084*K3**2 - 158*K4**2 - 20*K5**2 - 2*K6**2 + 3020 |
| 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}], [{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}], [{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 |