| Min(phi) over symmetries of the knot is: [-3,-1,0,1,1,2,0,2,1,3,3,1,0,1,0,0,1,1,-1,-1,1] |
| Flat knots (up to 7 crossings) with same phi are :['6.584'] |
| Arrow polynomial of the knot is: -14*K1**2 - 2*K1*K2 + K1 + 7*K2 + K3 + 8 |
| Flat knots (up to 7 crossings) with same arrow polynomial are :['6.584', '6.815', '6.976'] |
| Outer characteristic polynomial of the knot is: t^7+56t^5+45t^3+6t |
| Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.584'] |
| 2-strand cable arrow polynomial of the knot is: -192*K1**6 - 192*K1**4*K2**2 + 1536*K1**4*K2 - 5008*K1**4 + 288*K1**3*K2*K3 - 832*K1**3*K3 + 608*K1**2*K2**3 - 7296*K1**2*K2**2 - 288*K1**2*K2*K4 + 10888*K1**2*K2 - 592*K1**2*K3**2 - 32*K1**2*K3*K5 - 4296*K1**2 - 704*K1*K2**2*K3 - 32*K1*K2*K3*K4 + 7008*K1*K2*K3 + 736*K1*K3*K4 + 56*K1*K4*K5 - 1144*K2**4 - 176*K2**2*K3**2 - 8*K2**2*K4**2 + 1128*K2**2*K4 - 3782*K2**2 + 168*K2*K3*K5 + 8*K2*K4*K6 - 1596*K3**2 - 354*K4**2 - 52*K5**2 - 2*K6**2 + 4152 |
| Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.584'] |
| Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.11274', 'vk6.11352', 'vk6.12535', 'vk6.12646', 'vk6.17609', 'vk6.18929', 'vk6.19007', 'vk6.19355', 'vk6.19648', 'vk6.24067', 'vk6.24159', 'vk6.25525', 'vk6.25626', 'vk6.26127', 'vk6.26545', 'vk6.30948', 'vk6.31071', 'vk6.32124', 'vk6.32243', 'vk6.36406', 'vk6.37662', 'vk6.37711', 'vk6.43507', 'vk6.44780', 'vk6.52024', 'vk6.52114', 'vk6.52936', 'vk6.56494', 'vk6.56653', 'vk6.65386', 'vk6.66118', 'vk6.66154'] |
| 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 | O1O2O3O4U1O5U4O6U3U6U5U2 |
| R3 orbit | {'O1O2O3O4U1O5U4O6U3U6U5U2'} |
| R3 orbit length | 1 |
| Gauss code of -K | O1O2O3O4U3U5U6U2O6U1O5U4 |
| Gauss code of K* | O1O2O3O4U5U4U1U6O5U3O6U2 |
| Gauss code of -K* | O1O2O3O4U3O5U2O6U5U4U1U6 |
| 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 -1 0 2 1],[ 3 0 3 2 1 2 1],[-1 -3 0 -2 -1 2 1],[ 1 -2 2 0 0 3 1],[ 0 -1 1 0 0 1 0],[-2 -2 -2 -3 -1 0 0],[-1 -1 -1 -1 0 0 0]] |
| Primitive based matrix | [[ 0 2 1 1 0 -1 -3],[-2 0 0 -2 -1 -3 -2],[-1 0 0 -1 0 -1 -1],[-1 2 1 0 -1 -2 -3],[ 0 1 0 1 0 0 -1],[ 1 3 1 2 0 0 -2],[ 3 2 1 3 1 2 0]] |
| If based matrix primitive | True |
| Phi of primitive based matrix | [-2,-1,-1,0,1,3,0,2,1,3,2,1,0,1,1,1,2,3,0,1,2] |
| Phi over symmetry | [-3,-1,0,1,1,2,0,2,1,3,3,1,0,1,0,0,1,1,-1,-1,1] |
| Phi of -K | [-3,-1,0,1,1,2,0,2,1,3,3,1,0,1,0,0,1,1,-1,-1,1] |
| Phi of K* | [-2,-1,-1,0,1,3,-1,1,1,0,3,1,0,0,1,1,1,3,1,2,0] |
| Phi of -K* | [-3,-1,0,1,1,2,2,1,1,3,2,0,1,2,3,0,1,1,-1,0,2] |
| Symmetry type of based matrix | c |
| u-polynomial | t^3-t^2-t |
| Normalized Jones-Krushkal polynomial | 2z^2+21z+35 |
| Enhanced Jones-Krushkal polynomial | 2w^3z^2+21w^2z+35w |
| Inner characteristic polynomial | t^6+40t^4+16t^2+1 |
| Outer characteristic polynomial | t^7+56t^5+45t^3+6t |
| Flat arrow polynomial | -14*K1**2 - 2*K1*K2 + K1 + 7*K2 + K3 + 8 |
| 2-strand cable arrow polynomial | -192*K1**6 - 192*K1**4*K2**2 + 1536*K1**4*K2 - 5008*K1**4 + 288*K1**3*K2*K3 - 832*K1**3*K3 + 608*K1**2*K2**3 - 7296*K1**2*K2**2 - 288*K1**2*K2*K4 + 10888*K1**2*K2 - 592*K1**2*K3**2 - 32*K1**2*K3*K5 - 4296*K1**2 - 704*K1*K2**2*K3 - 32*K1*K2*K3*K4 + 7008*K1*K2*K3 + 736*K1*K3*K4 + 56*K1*K4*K5 - 1144*K2**4 - 176*K2**2*K3**2 - 8*K2**2*K4**2 + 1128*K2**2*K4 - 3782*K2**2 + 168*K2*K3*K5 + 8*K2*K4*K6 - 1596*K3**2 - 354*K4**2 - 52*K5**2 - 2*K6**2 + 4152 |
| 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}], [{1, 6}, {5}, {4}, {3}, {2}], [{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}], [{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}, {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}, {2, 4}, {3}, {1}], [{6}, {5}, {3, 4}, {1, 2}], [{6}, {5}, {4}, {3}, {1, 2}]] |
| If K is slice | False |