| Min(phi) over symmetries of the knot is: [-3,-2,0,1,1,3,0,2,2,3,3,2,1,2,2,0,0,2,-1,1,3] |
| Flat knots (up to 7 crossings) with same phi are :['6.216'] |
| Arrow polynomial of the knot is: -2*K1**2 - 4*K1*K2 + 2*K1 + K2 + 2*K3 + 2 |
| Flat knots (up to 7 crossings) with same arrow polynomial are :['6.120', '6.213', '6.216', '6.320', '6.322', '6.615', '6.617', '6.891', '6.951', '6.955', '6.1001', '6.1012', '6.1022', '6.1043', '6.1047', '6.1063', '6.1074', '6.1249', '6.1544', '6.1546', '6.1555', '6.1573', '6.1574', '6.1585', '6.1756', '6.1757', '6.1762', '6.1802', '6.1803', '6.1824', '6.1881', '6.1935'] |
| Outer characteristic polynomial of the knot is: t^7+60t^5+73t^3+14t |
| Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.216'] |
| 2-strand cable arrow polynomial of the knot is: -496*K1**4 + 1120*K1**3*K2*K3 - 256*K1**3*K3 - 704*K1**2*K2**2*K3**2 - 5328*K1**2*K2**2 + 224*K1**2*K2*K3**2 + 32*K1**2*K2*K3*K5 - 608*K1**2*K2*K4 + 4336*K1**2*K2 - 736*K1**2*K3**2 - 3120*K1**2 + 1600*K1*K2**3*K3 + 672*K1*K2**2*K3*K4 - 832*K1*K2**2*K3 - 32*K1*K2**2*K5 + 96*K1*K2*K3**3 - 320*K1*K2*K3*K4 + 6472*K1*K2*K3 + 792*K1*K3*K4 - 728*K2**4 - 1424*K2**2*K3**2 - 304*K2**2*K4**2 + 872*K2**2*K4 - 2244*K2**2 - 32*K2*K3**2*K4 + 408*K2*K3*K5 + 72*K2*K4*K6 - 16*K3**4 - 1844*K3**2 - 346*K4**2 - 4*K5**2 - 4*K6**2 + 2680 |
| Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.216'] |
| Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.4186', 'vk6.4265', 'vk6.5428', 'vk6.5546', 'vk6.7541', 'vk6.7621', 'vk6.9051', 'vk6.9130', 'vk6.18249', 'vk6.18586', 'vk6.24725', 'vk6.25140', 'vk6.36851', 'vk6.37316', 'vk6.44080', 'vk6.44421', 'vk6.48506', 'vk6.48585', 'vk6.49194', 'vk6.49302', 'vk6.50289', 'vk6.50361', 'vk6.51056', 'vk6.51087', 'vk6.56044', 'vk6.56320', 'vk6.60597', 'vk6.60942', 'vk6.65710', 'vk6.66006', 'vk6.68751', 'vk6.68961'] |
| 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 | O1O2O3O4O5U2O6U5U6U1U3U4 |
| R3 orbit | {'O1O2O3O4O5U2O6U5U6U1U3U4'} |
| R3 orbit length | 1 |
| Gauss code of -K | O1O2O3O4O5U2U3U5U6U1O6U4 |
| Gauss code of K* | O1O2O3O4O5U3U6U4U5U1O6U2 |
| Gauss code of -K* | O1O2O3O4O5U4O6U5U1U2U6U3 |
| 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 -3 1 3 0 1],[ 2 0 -1 2 3 0 1],[ 3 1 0 2 3 1 1],[-1 -2 -2 0 1 -1 1],[-3 -3 -3 -1 0 -1 1],[ 0 0 -1 1 1 0 1],[-1 -1 -1 -1 -1 -1 0]] |
| Primitive based matrix | [[ 0 3 1 1 0 -2 -3],[-3 0 1 -1 -1 -3 -3],[-1 -1 0 -1 -1 -1 -1],[-1 1 1 0 -1 -2 -2],[ 0 1 1 1 0 0 -1],[ 2 3 1 2 0 0 -1],[ 3 3 1 2 1 1 0]] |
| If based matrix primitive | True |
| Phi of primitive based matrix | [-3,-1,-1,0,2,3,-1,1,1,3,3,1,1,1,1,1,2,2,0,1,1] |
| Phi over symmetry | [-3,-2,0,1,1,3,0,2,2,3,3,2,1,2,2,0,0,2,-1,1,3] |
| Phi of -K | [-3,-2,0,1,1,3,0,2,2,3,3,2,1,2,2,0,0,2,-1,1,3] |
| Phi of K* | [-3,-1,-1,0,2,3,1,3,2,2,3,1,0,1,2,0,2,3,2,2,0] |
| Phi of -K* | [-3,-2,0,1,1,3,1,1,1,2,3,0,1,2,3,1,1,1,-1,-1,1] |
| Symmetry type of based matrix | c |
| u-polynomial | t^2-2t |
| Normalized Jones-Krushkal polynomial | 8z^2+29z+27 |
| Enhanced Jones-Krushkal polynomial | 8w^3z^2+29w^2z+27w |
| Inner characteristic polynomial | t^6+36t^4+20t^2+1 |
| Outer characteristic polynomial | t^7+60t^5+73t^3+14t |
| Flat arrow polynomial | -2*K1**2 - 4*K1*K2 + 2*K1 + K2 + 2*K3 + 2 |
| 2-strand cable arrow polynomial | -496*K1**4 + 1120*K1**3*K2*K3 - 256*K1**3*K3 - 704*K1**2*K2**2*K3**2 - 5328*K1**2*K2**2 + 224*K1**2*K2*K3**2 + 32*K1**2*K2*K3*K5 - 608*K1**2*K2*K4 + 4336*K1**2*K2 - 736*K1**2*K3**2 - 3120*K1**2 + 1600*K1*K2**3*K3 + 672*K1*K2**2*K3*K4 - 832*K1*K2**2*K3 - 32*K1*K2**2*K5 + 96*K1*K2*K3**3 - 320*K1*K2*K3*K4 + 6472*K1*K2*K3 + 792*K1*K3*K4 - 728*K2**4 - 1424*K2**2*K3**2 - 304*K2**2*K4**2 + 872*K2**2*K4 - 2244*K2**2 - 32*K2*K3**2*K4 + 408*K2*K3*K5 + 72*K2*K4*K6 - 16*K3**4 - 1844*K3**2 - 346*K4**2 - 4*K5**2 - 4*K6**2 + 2680 |
| 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}, {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}, {5}, {1, 4}, {2, 3}], [{6}, {5}, {1, 4}, {3}, {2}], [{6}, {5}, {2, 4}, {1, 3}], [{6}, {5}, {3, 4}, {1, 2}]] |
| If K is slice | False |