| Min(phi) over symmetries of the knot is: [-3,-1,-1,1,2,2,0,1,2,2,3,1,1,1,1,2,1,2,0,0,-1] |
| Flat knots (up to 7 crossings) with same phi are :['6.647'] |
| Arrow polynomial of the knot is: -8*K1**2 - 2*K1*K2 + K1 + 4*K2 + K3 + 5 |
| Flat knots (up to 7 crossings) with same arrow polynomial are :['6.377', '6.638', '6.646', '6.647', '6.657', '6.658', '6.662', '6.692', '6.695', '6.714', '6.720', '6.726', '6.730', '6.731', '6.749', '6.756', '6.772', '6.779', '6.781', '6.800', '6.829', '6.1085', '6.1089', '6.1302', '6.1349', '6.1350', '6.1360', '6.1362', '6.1375', '6.1384'] |
| Outer characteristic polynomial of the knot is: t^7+60t^5+92t^3+8t |
| Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.647'] |
| 2-strand cable arrow polynomial of the knot is: -64*K1**6 + 960*K1**4*K2 - 5296*K1**4 + 64*K1**3*K2*K3 - 640*K1**3*K3 + 384*K1**2*K2**3 + 32*K1**2*K2**2*K4 - 5744*K1**2*K2**2 - 704*K1**2*K2*K4 + 12016*K1**2*K2 - 240*K1**2*K3**2 - 64*K1**2*K4**2 - 6404*K1**2 - 640*K1*K2**2*K3 - 64*K1*K2**2*K5 - 32*K1*K2*K3*K4 + 7464*K1*K2*K3 + 1208*K1*K3*K4 + 80*K1*K4*K5 - 608*K2**4 - 48*K2**2*K3**2 - 8*K2**2*K4**2 + 1312*K2**2*K4 - 5750*K2**2 + 184*K2*K3*K5 + 8*K2*K4*K6 - 2368*K3**2 - 760*K4**2 - 84*K5**2 - 2*K6**2 + 5806 |
| Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.647'] |
| Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.20018', 'vk6.20061', 'vk6.21290', 'vk6.21341', 'vk6.27069', 'vk6.27126', 'vk6.28774', 'vk6.28813', 'vk6.38458', 'vk6.38527', 'vk6.40647', 'vk6.40722', 'vk6.45342', 'vk6.45427', 'vk6.47111', 'vk6.47167', 'vk6.56833', 'vk6.56882', 'vk6.57967', 'vk6.58018', 'vk6.61351', 'vk6.61412', 'vk6.62527', 'vk6.62567', 'vk6.66545', 'vk6.66590', 'vk6.67334', 'vk6.67379', 'vk6.69191', 'vk6.69242', 'vk6.69942', 'vk6.69981'] |
| 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 | O1O2O3O4U1O5U6U2O6U4U5U3 |
| R3 orbit | {'O1O2O3O4U1O5U6U2O6U4U5U3'} |
| R3 orbit length | 1 |
| Gauss code of -K | O1O2O3O4U2U5U1O6U3U6O5U4 |
| Gauss code of K* | O1O2O3U4U5U3U1O4U2O6O5U6 |
| Gauss code of -K* | O1O2O3U4O5O4U2O6U3U1U5U6 |
| 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 2 -1],[ 3 0 1 3 2 2 2],[ 1 -1 0 2 0 1 1],[-2 -3 -2 0 -1 1 -2],[-1 -2 0 1 0 1 -1],[-2 -2 -1 -1 -1 0 -2],[ 1 -2 -1 2 1 2 0]] |
| Primitive based matrix | [[ 0 2 2 1 -1 -1 -3],[-2 0 1 -1 -2 -2 -3],[-2 -1 0 -1 -1 -2 -2],[-1 1 1 0 0 -1 -2],[ 1 2 1 0 0 1 -1],[ 1 2 2 1 -1 0 -2],[ 3 3 2 2 1 2 0]] |
| If based matrix primitive | True |
| Phi of primitive based matrix | [-2,-2,-1,1,1,3,-1,1,2,2,3,1,1,2,2,0,1,2,-1,1,2] |
| Phi over symmetry | [-3,-1,-1,1,2,2,0,1,2,2,3,1,1,1,1,2,1,2,0,0,-1] |
| Phi of -K | [-3,-1,-1,1,2,2,0,1,2,2,3,1,1,1,1,2,1,2,0,0,-1] |
| Phi of K* | [-2,-2,-1,1,1,3,-1,0,1,2,3,0,1,1,2,1,2,2,-1,0,1] |
| Phi of -K* | [-3,-1,-1,1,2,2,1,2,2,2,3,1,0,1,2,1,2,2,1,1,-1] |
| Symmetry type of based matrix | c |
| u-polynomial | t^3-2t^2+t |
| Normalized Jones-Krushkal polynomial | z^2+22z+41 |
| Enhanced Jones-Krushkal polynomial | w^3z^2+22w^2z+41w |
| Inner characteristic polynomial | t^6+40t^4+46t^2+1 |
| Outer characteristic polynomial | t^7+60t^5+92t^3+8t |
| Flat arrow polynomial | -8*K1**2 - 2*K1*K2 + K1 + 4*K2 + K3 + 5 |
| 2-strand cable arrow polynomial | -64*K1**6 + 960*K1**4*K2 - 5296*K1**4 + 64*K1**3*K2*K3 - 640*K1**3*K3 + 384*K1**2*K2**3 + 32*K1**2*K2**2*K4 - 5744*K1**2*K2**2 - 704*K1**2*K2*K4 + 12016*K1**2*K2 - 240*K1**2*K3**2 - 64*K1**2*K4**2 - 6404*K1**2 - 640*K1*K2**2*K3 - 64*K1*K2**2*K5 - 32*K1*K2*K3*K4 + 7464*K1*K2*K3 + 1208*K1*K3*K4 + 80*K1*K4*K5 - 608*K2**4 - 48*K2**2*K3**2 - 8*K2**2*K4**2 + 1312*K2**2*K4 - 5750*K2**2 + 184*K2*K3*K5 + 8*K2*K4*K6 - 2368*K3**2 - 760*K4**2 - 84*K5**2 - 2*K6**2 + 5806 |
| 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}, {2, 5}, {4}, {3}, {1}], [{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}, {2, 4}, {1, 3}], [{6}, {5}, {3, 4}, {1, 2}], [{6}, {5}, {4}, {1, 3}, {2}]] |
| If K is slice | False |