| Min(phi) over symmetries of the knot is: [-3,-2,1,1,1,2,0,1,2,3,2,2,1,3,2,0,1,1,-1,0,1] |
| Flat knots (up to 7 crossings) with same phi are :['6.706'] |
| Arrow polynomial of the knot is: 4*K1**3 - 4*K1**2 - 2*K1*K2 - 2*K1 + 2*K2 + 3 |
| Flat knots (up to 7 crossings) with same arrow polynomial are :['6.520', '6.682', '6.706', '6.748', '6.1331'] |
| Outer characteristic polynomial of the knot is: t^7+56t^5+211t^3+6t |
| Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.706'] |
| 2-strand cable arrow polynomial of the knot is: -432*K1**4 - 256*K1**2*K2**4 + 928*K1**2*K2**3 + 64*K1**2*K2**2*K4 - 4352*K1**2*K2**2 - 128*K1**2*K2*K4 + 6488*K1**2*K2 - 16*K1**2*K3**2 - 48*K1**2*K4**2 - 5080*K1**2 + 480*K1*K2**3*K3 - 1152*K1*K2**2*K3 - 96*K1*K2**2*K5 - 32*K1*K2*K3*K4 + 4440*K1*K2*K3 + 512*K1*K3*K4 + 88*K1*K4*K5 - 32*K2**6 + 32*K2**4*K4 - 800*K2**4 - 160*K2**2*K3**2 - 8*K2**2*K4**2 + 856*K2**2*K4 - 3072*K2**2 + 48*K2*K3*K5 - 1260*K3**2 - 308*K4**2 - 36*K5**2 + 3330 |
| Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.706'] |
| Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.81595', 'vk6.81598', 'vk6.81680', 'vk6.81685', 'vk6.81746', 'vk6.81754', 'vk6.81759', 'vk6.81760', 'vk6.81981', 'vk6.81985', 'vk6.82286', 'vk6.82289', 'vk6.82401', 'vk6.82411', 'vk6.82433', 'vk6.82436', 'vk6.82517', 'vk6.82710', 'vk6.82717', 'vk6.83208', 'vk6.83613', 'vk6.84191', 'vk6.84198', 'vk6.84380', 'vk6.84398', 'vk6.85984', 'vk6.85990', 'vk6.88177', 'vk6.88752', 'vk6.88779', 'vk6.89121', 'vk6.89127'] |
| 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 | O1O2O3O4U5O6U3U1O5U2U6U4 |
| R3 orbit | {'O1O2O3O4U5O6U3U1O5U2U6U4'} |
| R3 orbit length | 1 |
| Gauss code of -K | O1O2O3O4U1U5U3O6U4U2O5U6 |
| Gauss code of K* | O1O2O3U4U1U5U3O6U2O5O4U6 |
| Gauss code of -K* | O1O2O3U4O5O6U2O4U1U6U3U5 |
| 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 3 -1 2],[ 2 0 0 0 3 1 2],[ 1 0 0 1 3 0 1],[ 1 0 -1 0 1 1 0],[-3 -3 -3 -1 0 -2 -1],[ 1 -1 0 -1 2 0 2],[-2 -2 -1 0 1 -2 0]] |
| Primitive based matrix | [[ 0 3 2 -1 -1 -1 -2],[-3 0 -1 -1 -2 -3 -3],[-2 1 0 0 -2 -1 -2],[ 1 1 0 0 1 -1 0],[ 1 2 2 -1 0 0 -1],[ 1 3 1 1 0 0 0],[ 2 3 2 0 1 0 0]] |
| If based matrix primitive | True |
| Phi of primitive based matrix | [-3,-2,1,1,1,2,1,1,2,3,3,0,2,1,2,-1,1,0,0,1,0] |
| Phi over symmetry | [-3,-2,1,1,1,2,0,1,2,3,2,2,1,3,2,0,1,1,-1,0,1] |
| Phi of -K | [-2,-1,-1,-1,2,3,0,1,1,2,2,0,1,1,2,-1,2,1,3,3,0] |
| Phi of K* | [-3,-2,1,1,1,2,0,1,2,3,2,2,1,3,2,0,1,1,-1,0,1] |
| Phi of -K* | [-2,-1,-1,-1,2,3,0,0,1,2,3,-1,1,0,1,0,1,3,2,2,1] |
| Symmetry type of based matrix | c |
| u-polynomial | -t^3+3t |
| Normalized Jones-Krushkal polynomial | 6z^2+25z+27 |
| Enhanced Jones-Krushkal polynomial | 6w^3z^2+25w^2z+27w |
| Inner characteristic polynomial | t^6+36t^4+113t^2+1 |
| Outer characteristic polynomial | t^7+56t^5+211t^3+6t |
| Flat arrow polynomial | 4*K1**3 - 4*K1**2 - 2*K1*K2 - 2*K1 + 2*K2 + 3 |
| 2-strand cable arrow polynomial | -432*K1**4 - 256*K1**2*K2**4 + 928*K1**2*K2**3 + 64*K1**2*K2**2*K4 - 4352*K1**2*K2**2 - 128*K1**2*K2*K4 + 6488*K1**2*K2 - 16*K1**2*K3**2 - 48*K1**2*K4**2 - 5080*K1**2 + 480*K1*K2**3*K3 - 1152*K1*K2**2*K3 - 96*K1*K2**2*K5 - 32*K1*K2*K3*K4 + 4440*K1*K2*K3 + 512*K1*K3*K4 + 88*K1*K4*K5 - 32*K2**6 + 32*K2**4*K4 - 800*K2**4 - 160*K2**2*K3**2 - 8*K2**2*K4**2 + 856*K2**2*K4 - 3072*K2**2 + 48*K2*K3*K5 - 1260*K3**2 - 308*K4**2 - 36*K5**2 + 3330 |
| 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}], [{3, 6}, {5}, {4}, {2}, {1}], [{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}, {4, 5}, {3}, {2}, {1}], [{6}, {5}, {1, 4}, {2, 3}], [{6}, {5}, {2, 4}, {1, 3}], [{6}, {5}, {2, 4}, {3}, {1}], [{6}, {5}, {3, 4}, {1, 2}]] |
| If K is slice | False |