| Min(phi) over symmetries of the knot is: [-3,0,0,0,1,2,0,1,2,2,2,1,0,0,0,0,0,0,1,1,1] |
| Flat knots (up to 7 crossings) with same phi are :['6.992'] |
| Arrow polynomial of the knot is: 8*K1**3 - 6*K1**2 - 6*K1*K2 - 3*K1 + 3*K2 + K3 + 4 |
| Flat knots (up to 7 crossings) with same arrow polynomial are :['6.237', '6.602', '6.956', '6.986', '6.992', '6.1052', '6.1059'] |
| Outer characteristic polynomial of the knot is: t^7+53t^5+38t^3+6t |
| Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.992'] |
| 2-strand cable arrow polynomial of the knot is: 96*K1**4*K2 - 1616*K1**4 + 64*K1**3*K2*K3 - 352*K1**3*K3 - 256*K1**2*K2**4 + 896*K1**2*K2**3 - 6000*K1**2*K2**2 - 352*K1**2*K2*K4 + 8728*K1**2*K2 - 272*K1**2*K3**2 - 5988*K1**2 + 768*K1*K2**3*K3 + 32*K1*K2**2*K3*K4 - 768*K1*K2**2*K3 - 32*K1*K2**2*K5 - 224*K1*K2*K3*K4 - 32*K1*K2*K3*K6 + 7056*K1*K2*K3 + 560*K1*K3*K4 + 24*K1*K4*K5 - 64*K2**6 + 96*K2**4*K4 - 1528*K2**4 - 800*K2**2*K3**2 - 72*K2**2*K4**2 + 1312*K2**2*K4 - 3882*K2**2 + 512*K2*K3*K5 + 32*K2*K4*K6 + 8*K3**2*K6 - 1972*K3**2 - 342*K4**2 - 80*K5**2 - 6*K6**2 + 4452 |
| Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.992'] |
| Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.73360', 'vk6.73389', 'vk6.73523', 'vk6.73566', 'vk6.73718', 'vk6.73837', 'vk6.74250', 'vk6.74878', 'vk6.75329', 'vk6.75532', 'vk6.75839', 'vk6.76427', 'vk6.78244', 'vk6.78315', 'vk6.78493', 'vk6.78634', 'vk6.78829', 'vk6.79298', 'vk6.80067', 'vk6.80099', 'vk6.80217', 'vk6.80264', 'vk6.80398', 'vk6.80763', 'vk6.81946', 'vk6.82673', 'vk6.84741', 'vk6.85037', 'vk6.85155', 'vk6.86517', 'vk6.87355', 'vk6.89420'] |
| 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 | O1O2O3O4U1U5O6U3O5U4U2U6 |
| R3 orbit | {'O1O2O3O4U1U5O6U3O5U4U2U6'} |
| R3 orbit length | 1 |
| Gauss code of -K | O1O2O3O4U5U3U1O6U2O5U6U4 |
| Gauss code of K* | O1O2O3U4U2U5U1O4O6U3O5U6 |
| Gauss code of -K* | O1O2O3U4O5U1O4O6U3U5U2U6 |
| 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 0 0 1 0 2],[ 3 0 3 1 2 2 3],[ 0 -3 0 0 1 -1 2],[ 0 -1 0 0 0 0 1],[-1 -2 -1 0 0 -1 0],[ 0 -2 1 0 1 0 2],[-2 -3 -2 -1 0 -2 0]] |
| Primitive based matrix | [[ 0 2 1 0 0 0 -3],[-2 0 0 -1 -2 -2 -3],[-1 0 0 0 -1 -1 -2],[ 0 1 0 0 0 0 -1],[ 0 2 1 0 0 1 -2],[ 0 2 1 0 -1 0 -3],[ 3 3 2 1 2 3 0]] |
| If based matrix primitive | True |
| Phi of primitive based matrix | [-2,-1,0,0,0,3,0,1,2,2,3,0,1,1,2,0,0,1,-1,2,3] |
| Phi over symmetry | [-3,0,0,0,1,2,0,1,2,2,2,1,0,0,0,0,0,0,1,1,1] |
| Phi of -K | [-3,0,0,0,1,2,0,1,2,2,2,1,0,0,0,0,0,0,1,1,1] |
| Phi of K* | [-2,-1,0,0,0,3,1,0,0,1,2,0,0,1,2,-1,0,0,0,1,2] |
| Phi of -K* | [-3,0,0,0,1,2,1,2,3,2,3,0,0,0,1,1,1,2,1,2,0] |
| Symmetry type of based matrix | c |
| u-polynomial | t^3-t^2-t |
| Normalized Jones-Krushkal polynomial | 4z^2+23z+31 |
| Enhanced Jones-Krushkal polynomial | 4w^3z^2+23w^2z+31w |
| Inner characteristic polynomial | t^6+39t^4+15t^2+1 |
| Outer characteristic polynomial | t^7+53t^5+38t^3+6t |
| Flat arrow polynomial | 8*K1**3 - 6*K1**2 - 6*K1*K2 - 3*K1 + 3*K2 + K3 + 4 |
| 2-strand cable arrow polynomial | 96*K1**4*K2 - 1616*K1**4 + 64*K1**3*K2*K3 - 352*K1**3*K3 - 256*K1**2*K2**4 + 896*K1**2*K2**3 - 6000*K1**2*K2**2 - 352*K1**2*K2*K4 + 8728*K1**2*K2 - 272*K1**2*K3**2 - 5988*K1**2 + 768*K1*K2**3*K3 + 32*K1*K2**2*K3*K4 - 768*K1*K2**2*K3 - 32*K1*K2**2*K5 - 224*K1*K2*K3*K4 - 32*K1*K2*K3*K6 + 7056*K1*K2*K3 + 560*K1*K3*K4 + 24*K1*K4*K5 - 64*K2**6 + 96*K2**4*K4 - 1528*K2**4 - 800*K2**2*K3**2 - 72*K2**2*K4**2 + 1312*K2**2*K4 - 3882*K2**2 + 512*K2*K3*K5 + 32*K2*K4*K6 + 8*K3**2*K6 - 1972*K3**2 - 342*K4**2 - 80*K5**2 - 6*K6**2 + 4452 |
| 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}], [{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}, {3, 4}, {1, 2}], [{6}, {5}, {3, 4}, {2}, {1}], [{6}, {5}, {4}, {1, 3}, {2}]] |
| If K is slice | False |