| Min(phi) over symmetries of the knot is: [-3,-1,0,1,1,2,0,2,1,3,3,2,1,1,2,1,1,1,0,-1,1] |
| Flat knots (up to 7 crossings) with same phi are :['6.696'] |
| Arrow polynomial of the knot is: 8*K1**3 - 2*K1**2 - 6*K1*K2 - 3*K1 + K2 + K3 + 2 |
| Flat knots (up to 7 crossings) with same arrow polynomial are :['6.677', '6.696', '6.738', '6.758'] |
| Outer characteristic polynomial of the knot is: t^7+54t^5+135t^3+18t |
| Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.696'] |
| 2-strand cable arrow polynomial of the knot is: -16*K1**4 - 1472*K1**2*K2**4 + 1760*K1**2*K2**3 - 6320*K1**2*K2**2 - 192*K1**2*K2*K4 + 4272*K1**2*K2 - 16*K1**2*K3**2 - 2820*K1**2 + 1952*K1*K2**3*K3 + 32*K1*K2**2*K3*K4 - 800*K1*K2**2*K3 - 32*K1*K2**2*K5 - 320*K1*K2*K3*K4 - 32*K1*K2*K3*K6 + 5504*K1*K2*K3 + 424*K1*K3*K4 + 40*K1*K4*K5 - 448*K2**6 + 448*K2**4*K4 - 2776*K2**4 - 768*K2**2*K3**2 - 216*K2**2*K4**2 + 2192*K2**2*K4 - 1190*K2**2 + 280*K2*K3*K5 + 72*K2*K4*K6 + 8*K3**2*K6 - 1456*K3**2 - 558*K4**2 - 28*K5**2 - 10*K6**2 + 2484 |
| Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.696'] |
| Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.10507', 'vk6.10514', 'vk6.10574', 'vk6.10589', 'vk6.10761', 'vk6.10778', 'vk6.10882', 'vk6.10891', 'vk6.17677', 'vk6.17689', 'vk6.17724', 'vk6.17736', 'vk6.24287', 'vk6.24299', 'vk6.30188', 'vk6.30195', 'vk6.30253', 'vk6.30268', 'vk6.30380', 'vk6.30397', 'vk6.36513', 'vk6.36525', 'vk6.43619', 'vk6.43635', 'vk6.43721', 'vk6.43739', 'vk6.60353', 'vk6.60363', 'vk6.63452', 'vk6.63459', 'vk6.65420', 'vk6.65422'] |
| 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 | O1O2O3O4U3O5U6U4O6U1U2U5 |
| R3 orbit | {'O1O2O3O4U3O5U6U4O6U1U2U5'} |
| R3 orbit length | 1 |
| Gauss code of -K | O1O2O3O4U5U3U4O6U1U6O5U2 |
| Gauss code of K* | O1O2O3U1U2U4U5O4U3O6O5U6 |
| Gauss code of -K* | O1O2O3U4O5O4U1O6U5U6U2U3 |
| 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 0 -1 1 3 -1],[ 2 0 1 -1 2 3 1],[ 0 -1 0 -1 2 2 -1],[ 1 1 1 0 1 1 0],[-1 -2 -2 -1 0 0 -1],[-3 -3 -2 -1 0 0 -3],[ 1 -1 1 0 1 3 0]] |
| Primitive based matrix | [[ 0 3 1 0 -1 -1 -2],[-3 0 0 -2 -1 -3 -3],[-1 0 0 -2 -1 -1 -2],[ 0 2 2 0 -1 -1 -1],[ 1 1 1 1 0 0 1],[ 1 3 1 1 0 0 -1],[ 2 3 2 1 -1 1 0]] |
| If based matrix primitive | True |
| Phi of primitive based matrix | [-3,-1,0,1,1,2,0,2,1,3,3,2,1,1,2,1,1,1,0,-1,1] |
| Phi over symmetry | [-3,-1,0,1,1,2,0,2,1,3,3,2,1,1,2,1,1,1,0,-1,1] |
| Phi of -K | [-2,-1,-1,0,1,3,0,2,1,1,2,0,0,1,1,0,1,3,-1,1,2] |
| Phi of K* | [-3,-1,0,1,1,2,2,1,1,3,2,-1,1,1,1,0,0,1,0,0,2] |
| Phi of -K* | [-2,-1,-1,0,1,3,-1,1,1,2,3,0,1,1,1,1,1,3,2,2,0] |
| Symmetry type of based matrix | c |
| u-polynomial | -t^3+t^2+t |
| Normalized Jones-Krushkal polynomial | z^2+6z+9 |
| Enhanced Jones-Krushkal polynomial | -4w^4z^2+5w^3z^2-16w^3z+22w^2z+9w |
| Inner characteristic polynomial | t^6+38t^4+76t^2+4 |
| Outer characteristic polynomial | t^7+54t^5+135t^3+18t |
| Flat arrow polynomial | 8*K1**3 - 2*K1**2 - 6*K1*K2 - 3*K1 + K2 + K3 + 2 |
| 2-strand cable arrow polynomial | -16*K1**4 - 1472*K1**2*K2**4 + 1760*K1**2*K2**3 - 6320*K1**2*K2**2 - 192*K1**2*K2*K4 + 4272*K1**2*K2 - 16*K1**2*K3**2 - 2820*K1**2 + 1952*K1*K2**3*K3 + 32*K1*K2**2*K3*K4 - 800*K1*K2**2*K3 - 32*K1*K2**2*K5 - 320*K1*K2*K3*K4 - 32*K1*K2*K3*K6 + 5504*K1*K2*K3 + 424*K1*K3*K4 + 40*K1*K4*K5 - 448*K2**6 + 448*K2**4*K4 - 2776*K2**4 - 768*K2**2*K3**2 - 216*K2**2*K4**2 + 2192*K2**2*K4 - 1190*K2**2 + 280*K2*K3*K5 + 72*K2*K4*K6 + 8*K3**2*K6 - 1456*K3**2 - 558*K4**2 - 28*K5**2 - 10*K6**2 + 2484 |
| 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}, {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}, {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}]] |
| If K is slice | False |