| Min(phi) over symmetries of the knot is: [-3,-1,0,1,1,2,1,1,2,3,1,1,2,2,2,0,0,1,0,2,2] |
| Flat knots (up to 7 crossings) with same phi are :['6.362'] |
| Arrow polynomial of the knot is: 4*K1**3 - 2*K1**2 - 6*K1*K2 + K2 + 2*K3 + 2 |
| Flat knots (up to 7 crossings) with same arrow polynomial are :['6.362', '6.624', '6.789', '6.859', '6.882', '6.975', '6.989', '6.1048', '6.1057', '6.1158'] |
| Outer characteristic polynomial of the knot is: t^7+54t^5+59t^3+3t |
| Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.362'] |
| 2-strand cable arrow polynomial of the knot is: 96*K1**2*K2**3 - 1712*K1**2*K2**2 + 2200*K1**2*K2 - 16*K1**2*K3**2 - 2036*K1**2 + 512*K1*K2**3*K3 - 608*K1*K2**2*K3 - 64*K1*K2**2*K5 - 128*K1*K2*K3*K4 + 2512*K1*K2*K3 + 336*K1*K3*K4 + 32*K1*K4*K5 - 32*K2**6 + 64*K2**4*K4 - 504*K2**4 - 32*K2**3*K6 - 352*K2**2*K3**2 - 24*K2**2*K4**2 + 864*K2**2*K4 - 1656*K2**2 - 32*K2*K3**2*K4 + 160*K2*K3*K5 + 32*K2*K4*K6 - 16*K3**4 + 24*K3**2*K6 - 884*K3**2 - 354*K4**2 - 24*K5**2 - 8*K6**2 + 1648 |
| Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.362'] |
| Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.11081', 'vk6.11159', 'vk6.12245', 'vk6.12352', 'vk6.18332', 'vk6.18669', 'vk6.24766', 'vk6.25223', 'vk6.30658', 'vk6.30749', 'vk6.31334', 'vk6.31743', 'vk6.31884', 'vk6.31952', 'vk6.32502', 'vk6.32905', 'vk6.36948', 'vk6.37410', 'vk6.39646', 'vk6.41885', 'vk6.44139', 'vk6.44460', 'vk6.46242', 'vk6.47847', 'vk6.51915', 'vk6.52332', 'vk6.52842', 'vk6.53180', 'vk6.56329', 'vk6.57616', 'vk6.60956', 'vk6.62284', 'vk6.63524', 'vk6.63568', 'vk6.64004', 'vk6.64048', 'vk6.65752', 'vk6.66016', 'vk6.68760', 'vk6.68968'] |
| 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 | O1O2O3O4O5U3U4O6U5U2U1U6 |
| R3 orbit | {'O1O2O3O4O5U3U4O6U5U2U1U6', 'O1O2O3O4U2O5U4O6U3U5U1U6'} |
| R3 orbit length | 2 |
| Gauss code of -K | O1O2O3O4O5U6U5U4U1O6U2U3 |
| Gauss code of K* | O1O2O3O4U3U2U5U6U1O5O6U4 |
| Gauss code of -K* | O1O2O3O4U1O5O6U4U5U6U3U2 |
| 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 -1 -1 -2 0 1 3],[ 1 0 0 -2 0 2 3],[ 1 0 0 -2 0 2 2],[ 2 2 2 0 1 2 1],[ 0 0 0 -1 0 1 1],[-1 -2 -2 -2 -1 0 1],[-3 -3 -2 -1 -1 -1 0]] |
| Primitive based matrix | [[ 0 3 1 0 -1 -1 -2],[-3 0 -1 -1 -2 -3 -1],[-1 1 0 -1 -2 -2 -2],[ 0 1 1 0 0 0 -1],[ 1 2 2 0 0 0 -2],[ 1 3 2 0 0 0 -2],[ 2 1 2 1 2 2 0]] |
| If based matrix primitive | True |
| Phi of primitive based matrix | [-3,-1,0,1,1,2,1,1,2,3,1,1,2,2,2,0,0,1,0,2,2] |
| Phi over symmetry | [-3,-1,0,1,1,2,1,1,2,3,1,1,2,2,2,0,0,1,0,2,2] |
| Phi of -K | [-2,-1,-1,0,1,3,-1,-1,1,1,4,0,1,0,1,1,0,2,0,2,1] |
| Phi of K* | [-3,-1,0,1,1,2,1,2,1,2,4,0,0,0,1,1,1,1,0,-1,-1] |
| Phi of -K* | [-2,-1,-1,0,1,3,2,2,1,2,1,0,0,2,2,0,2,3,1,1,1] |
| Symmetry type of based matrix | c |
| u-polynomial | -t^3+t^2+t |
| Normalized Jones-Krushkal polynomial | 5z^2+18z+17 |
| Enhanced Jones-Krushkal polynomial | 5w^3z^2+18w^2z+17w |
| Inner characteristic polynomial | t^6+38t^4+14t^2 |
| Outer characteristic polynomial | t^7+54t^5+59t^3+3t |
| Flat arrow polynomial | 4*K1**3 - 2*K1**2 - 6*K1*K2 + K2 + 2*K3 + 2 |
| 2-strand cable arrow polynomial | 96*K1**2*K2**3 - 1712*K1**2*K2**2 + 2200*K1**2*K2 - 16*K1**2*K3**2 - 2036*K1**2 + 512*K1*K2**3*K3 - 608*K1*K2**2*K3 - 64*K1*K2**2*K5 - 128*K1*K2*K3*K4 + 2512*K1*K2*K3 + 336*K1*K3*K4 + 32*K1*K4*K5 - 32*K2**6 + 64*K2**4*K4 - 504*K2**4 - 32*K2**3*K6 - 352*K2**2*K3**2 - 24*K2**2*K4**2 + 864*K2**2*K4 - 1656*K2**2 - 32*K2*K3**2*K4 + 160*K2*K3*K5 + 32*K2*K4*K6 - 16*K3**4 + 24*K3**2*K6 - 884*K3**2 - 354*K4**2 - 24*K5**2 - 8*K6**2 + 1648 |
| 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}], [{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}, {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}, {1, 4}, {3}, {2}], [{6}, {5}, {2, 4}, {1, 3}], [{6}, {5}, {3, 4}, {1, 2}]] |
| If K is slice | False |