| Min(phi) over symmetries of the knot is: [-3,-1,0,1,1,2,0,0,2,3,4,0,0,2,1,0,1,0,0,0,1] |
| Flat knots (up to 7 crossings) with same phi are :['6.982'] |
| Arrow polynomial of the knot is: 4*K1**3 - 6*K1**2 - 6*K1*K2 + 3*K2 + 2*K3 + 4 |
| Flat knots (up to 7 crossings) with same arrow polynomial are :['6.311', '6.528', '6.536', '6.817', '6.982', '6.984', '6.1284'] |
| Outer characteristic polynomial of the knot is: t^7+50t^5+62t^3+8t |
| Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.982'] |
| 2-strand cable arrow polynomial of the knot is: -384*K1**4*K2**2 + 1280*K1**4*K2 - 2768*K1**4 + 480*K1**3*K2*K3 + 32*K1**3*K3*K4 - 992*K1**3*K3 - 192*K1**2*K2**4 + 1056*K1**2*K2**3 - 7840*K1**2*K2**2 - 1408*K1**2*K2*K4 + 10816*K1**2*K2 - 368*K1**2*K3**2 - 144*K1**2*K4**2 - 7516*K1**2 + 416*K1*K2**3*K3 - 1152*K1*K2**2*K3 - 384*K1*K2**2*K5 - 64*K1*K2*K3*K4 + 9936*K1*K2*K3 + 1920*K1*K3*K4 + 304*K1*K4*K5 + 8*K1*K5*K6 - 32*K2**6 + 64*K2**4*K4 - 1368*K2**4 - 32*K2**3*K6 - 272*K2**2*K3**2 - 24*K2**2*K4**2 + 2360*K2**2*K4 - 5868*K2**2 + 488*K2*K3*K5 + 48*K2*K4*K6 + 16*K3**2*K6 - 3040*K3**2 - 1250*K4**2 - 228*K5**2 - 28*K6**2 + 6128 |
| Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.982'] |
| Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.11434', 'vk6.11731', 'vk6.12748', 'vk6.13093', 'vk6.20332', 'vk6.21674', 'vk6.27635', 'vk6.29180', 'vk6.31181', 'vk6.31524', 'vk6.32349', 'vk6.32768', 'vk6.39057', 'vk6.41315', 'vk6.45813', 'vk6.47485', 'vk6.52187', 'vk6.52446', 'vk6.53018', 'vk6.53336', 'vk6.57203', 'vk6.58419', 'vk6.61816', 'vk6.62943', 'vk6.63753', 'vk6.63865', 'vk6.64181', 'vk6.64369', 'vk6.66810', 'vk6.67679', 'vk6.69449', 'vk6.70172'] |
| 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 | O1O2O3O4U1U4O5U2O6U3U5U6 |
| R3 orbit | {'O1O2O3O4U1U4O5U2O6U3U5U6'} |
| R3 orbit length | 1 |
| Gauss code of -K | O1O2O3O4U5U6U2O5U3O6U1U4 |
| Gauss code of K* | O1O2O3U4U5U1U6O4O6U2O5U3 |
| Gauss code of -K* | O1O2O3U1O4U2O5O6U5U3U4U6 |
| 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 -1 0 1 1 2],[ 3 0 2 3 1 2 1],[ 1 -2 0 1 0 2 2],[ 0 -3 -1 0 0 1 2],[-1 -1 0 0 0 0 0],[-1 -2 -2 -1 0 0 1],[-2 -1 -2 -2 0 -1 0]] |
| Primitive based matrix | [[ 0 2 1 1 0 -1 -3],[-2 0 0 -1 -2 -2 -1],[-1 0 0 0 0 0 -1],[-1 1 0 0 -1 -2 -2],[ 0 2 0 1 0 -1 -3],[ 1 2 0 2 1 0 -2],[ 3 1 1 2 3 2 0]] |
| If based matrix primitive | True |
| Phi of primitive based matrix | [-2,-1,-1,0,1,3,0,1,2,2,1,0,0,0,1,1,2,2,1,3,2] |
| Phi over symmetry | [-3,-1,0,1,1,2,0,0,2,3,4,0,0,2,1,0,1,0,0,0,1] |
| Phi of -K | [-3,-1,0,1,1,2,0,0,2,3,4,0,0,2,1,0,1,0,0,0,1] |
| Phi of K* | [-2,-1,-1,0,1,3,0,1,0,1,4,0,0,0,2,1,2,3,0,0,0] |
| Phi of -K* | [-3,-1,0,1,1,2,2,3,1,2,1,1,0,2,2,0,1,2,0,0,1] |
| Symmetry type of based matrix | c |
| u-polynomial | t^3-t^2-t |
| Normalized Jones-Krushkal polynomial | 5z^2+26z+33 |
| Enhanced Jones-Krushkal polynomial | 5w^3z^2+26w^2z+33w |
| Inner characteristic polynomial | t^6+34t^4+21t^2+1 |
| Outer characteristic polynomial | t^7+50t^5+62t^3+8t |
| Flat arrow polynomial | 4*K1**3 - 6*K1**2 - 6*K1*K2 + 3*K2 + 2*K3 + 4 |
| 2-strand cable arrow polynomial | -384*K1**4*K2**2 + 1280*K1**4*K2 - 2768*K1**4 + 480*K1**3*K2*K3 + 32*K1**3*K3*K4 - 992*K1**3*K3 - 192*K1**2*K2**4 + 1056*K1**2*K2**3 - 7840*K1**2*K2**2 - 1408*K1**2*K2*K4 + 10816*K1**2*K2 - 368*K1**2*K3**2 - 144*K1**2*K4**2 - 7516*K1**2 + 416*K1*K2**3*K3 - 1152*K1*K2**2*K3 - 384*K1*K2**2*K5 - 64*K1*K2*K3*K4 + 9936*K1*K2*K3 + 1920*K1*K3*K4 + 304*K1*K4*K5 + 8*K1*K5*K6 - 32*K2**6 + 64*K2**4*K4 - 1368*K2**4 - 32*K2**3*K6 - 272*K2**2*K3**2 - 24*K2**2*K4**2 + 2360*K2**2*K4 - 5868*K2**2 + 488*K2*K3*K5 + 48*K2*K4*K6 + 16*K3**2*K6 - 3040*K3**2 - 1250*K4**2 - 228*K5**2 - 28*K6**2 + 6128 |
| 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}], [{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}, {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}, {2, 4}, {3}, {1}], [{6}, {5}, {3, 4}, {1, 2}], [{6}, {5}, {4}, {1, 3}, {2}]] |
| If K is slice | False |