| Min(phi) over symmetries of the knot is: [-3,-2,0,1,2,2,0,1,2,1,3,0,3,2,3,0,1,0,0,1,0] |
| Flat knots (up to 7 crossings) with same phi are :['6.622'] |
| Arrow polynomial of the knot is: 8*K1**3 - 10*K1**2 - 6*K1*K2 - 3*K1 + 5*K2 + K3 + 6 |
| Flat knots (up to 7 crossings) with same arrow polynomial are :['6.576', '6.581', '6.622', '6.627', '6.983', '6.1017'] |
| Outer characteristic polynomial of the knot is: t^7+67t^5+293t^3+9t |
| Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.622'] |
| 2-strand cable arrow polynomial of the knot is: 96*K1**4*K2 - 1152*K1**4 + 64*K1**3*K2*K3 - 224*K1**3*K3 - 256*K1**2*K2**4 + 1056*K1**2*K2**3 + 96*K1**2*K2**2*K4 - 5504*K1**2*K2**2 + 32*K1**2*K2*K3**2 - 288*K1**2*K2*K4 + 9136*K1**2*K2 - 128*K1**2*K3**2 - 32*K1**2*K4**2 - 7120*K1**2 + 512*K1*K2**3*K3 + 32*K1*K2**2*K3*K4 - 2016*K1*K2**2*K3 - 288*K1*K2**2*K5 - 64*K1*K2*K3*K4 + 7616*K1*K2*K3 + 880*K1*K3*K4 + 96*K1*K4*K5 - 64*K2**6 + 96*K2**4*K4 - 1736*K2**4 - 32*K2**3*K6 - 416*K2**2*K3**2 - 40*K2**2*K4**2 + 2224*K2**2*K4 - 5066*K2**2 - 32*K2*K3**2*K4 + 376*K2*K3*K5 + 32*K2*K4*K6 + 8*K3**2*K6 - 2376*K3**2 - 654*K4**2 - 104*K5**2 - 6*K6**2 + 5244 |
| Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.622'] |
| Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.73357', 'vk6.73388', 'vk6.73519', 'vk6.73567', 'vk6.73714', 'vk6.73833', 'vk6.74266', 'vk6.74890', 'vk6.75328', 'vk6.75529', 'vk6.75833', 'vk6.76443', 'vk6.78247', 'vk6.78314', 'vk6.78497', 'vk6.78626', 'vk6.78821', 'vk6.79310', 'vk6.80071', 'vk6.80098', 'vk6.80220', 'vk6.80256', 'vk6.80394', 'vk6.80775', 'vk6.81959', 'vk6.82690', 'vk6.84750', 'vk6.85050', 'vk6.85157', 'vk6.86531', 'vk6.87352', 'vk6.89449'] |
| 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 | O1O2O3O4U5O6U2O5U1U4U6U3 |
| R3 orbit | {'O1O2O3O4U5O6U2O5U1U4U6U3'} |
| R3 orbit length | 1 |
| Gauss code of -K | O1O2O3O4U2U5U1U4O6U3O5U6 |
| Gauss code of K* | O1O2O3O4U1U5U4U2O6U3O5U6 |
| Gauss code of -K* | O1O2O3O4U5O6U2O5U3U1U6U4 |
| 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 -2 2 1 0 2],[ 3 0 1 4 2 2 2],[ 2 -1 0 2 0 2 1],[-2 -4 -2 0 -1 -1 0],[-1 -2 0 1 0 -1 0],[ 0 -2 -2 1 1 0 2],[-2 -2 -1 0 0 -2 0]] |
| Primitive based matrix | [[ 0 2 2 1 0 -2 -3],[-2 0 0 0 -2 -1 -2],[-2 0 0 -1 -1 -2 -4],[-1 0 1 0 -1 0 -2],[ 0 2 1 1 0 -2 -2],[ 2 1 2 0 2 0 -1],[ 3 2 4 2 2 1 0]] |
| If based matrix primitive | True |
| Phi of primitive based matrix | [-2,-2,-1,0,2,3,0,0,2,1,2,1,1,2,4,1,0,2,2,2,1] |
| Phi over symmetry | [-3,-2,0,1,2,2,0,1,2,1,3,0,3,2,3,0,1,0,0,1,0] |
| Phi of -K | [-3,-2,0,1,2,2,0,1,2,1,3,0,3,2,3,0,1,0,0,1,0] |
| Phi of K* | [-2,-2,-1,0,2,3,0,0,1,2,1,1,0,3,3,0,3,2,0,1,0] |
| Phi of -K* | [-3,-2,0,1,2,2,1,2,2,2,4,2,0,1,2,1,2,1,0,1,0] |
| Symmetry type of based matrix | c |
| u-polynomial | t^3-t^2-t |
| Normalized Jones-Krushkal polynomial | 3z^2+22z+33 |
| Enhanced Jones-Krushkal polynomial | 3w^3z^2+22w^2z+33w |
| Inner characteristic polynomial | t^6+45t^4+170t^2+4 |
| Outer characteristic polynomial | t^7+67t^5+293t^3+9t |
| Flat arrow polynomial | 8*K1**3 - 10*K1**2 - 6*K1*K2 - 3*K1 + 5*K2 + K3 + 6 |
| 2-strand cable arrow polynomial | 96*K1**4*K2 - 1152*K1**4 + 64*K1**3*K2*K3 - 224*K1**3*K3 - 256*K1**2*K2**4 + 1056*K1**2*K2**3 + 96*K1**2*K2**2*K4 - 5504*K1**2*K2**2 + 32*K1**2*K2*K3**2 - 288*K1**2*K2*K4 + 9136*K1**2*K2 - 128*K1**2*K3**2 - 32*K1**2*K4**2 - 7120*K1**2 + 512*K1*K2**3*K3 + 32*K1*K2**2*K3*K4 - 2016*K1*K2**2*K3 - 288*K1*K2**2*K5 - 64*K1*K2*K3*K4 + 7616*K1*K2*K3 + 880*K1*K3*K4 + 96*K1*K4*K5 - 64*K2**6 + 96*K2**4*K4 - 1736*K2**4 - 32*K2**3*K6 - 416*K2**2*K3**2 - 40*K2**2*K4**2 + 2224*K2**2*K4 - 5066*K2**2 - 32*K2*K3**2*K4 + 376*K2*K3*K5 + 32*K2*K4*K6 + 8*K3**2*K6 - 2376*K3**2 - 654*K4**2 - 104*K5**2 - 6*K6**2 + 5244 |
| 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}], [{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}], [{5, 6}, {4}, {3}, {2}, {1}], [{6}, {1, 5}, {2, 4}, {3}], [{6}, {1, 5}, {3, 4}, {2}], [{6}, {1, 5}, {4}, {2, 3}], [{6}, {1, 5}, {4}, {3}, {2}], [{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}, {2, 4}, {1, 3}], [{6}, {5}, {3, 4}, {1, 2}], [{6}, {5}, {4}, {1, 3}, {2}]] |
| If K is slice | False |