| Min(phi) over symmetries of the knot is: [-2,-2,0,1,1,2,0,1,1,1,2,1,1,2,2,1,1,2,0,0,0] |
| Flat knots (up to 7 crossings) with same phi are :['6.1319'] |
| Arrow polynomial of the knot is: -6*K1**2 - 4*K1*K2 + 2*K1 + 3*K2 + 2*K3 + 4 |
| Flat knots (up to 7 crossings) with same arrow polynomial are :['6.239', '6.428', '6.470', '6.556', '6.700', '6.910', '6.962', '6.1006', '6.1013', '6.1038', '6.1207', '6.1224', '6.1225', '6.1269', '6.1270', '6.1308', '6.1319', '6.1320', '6.1323', '6.1485', '6.1551', '6.1579', '6.1581', '6.1660', '6.1672', '6.1679', '6.1711', '6.1719', '6.1732', '6.1745', '6.1748', '6.1827', '6.1836', '6.1838', '6.1850', '6.1866'] |
| Outer characteristic polynomial of the knot is: t^7+37t^5+32t^3+5t |
| Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.1319'] |
| 2-strand cable arrow polynomial of the knot is: -64*K1**6 + 928*K1**4*K2 - 4032*K1**4 + 32*K1**3*K2*K3 - 1120*K1**3*K3 - 2640*K1**2*K2**2 - 576*K1**2*K2*K4 + 9400*K1**2*K2 - 800*K1**2*K3**2 - 512*K1**2*K4**2 - 6420*K1**2 - 288*K1*K2**2*K3 - 128*K1*K2*K3*K4 + 6048*K1*K2*K3 + 2168*K1*K3*K4 + 456*K1*K4*K5 - 120*K2**4 - 48*K2**2*K3**2 - 48*K2**2*K4**2 + 768*K2**2*K4 - 4956*K2**2 + 72*K2*K3*K5 + 32*K2*K4*K6 - 2384*K3**2 - 958*K4**2 - 92*K5**2 - 4*K6**2 + 5284 |
| Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.1319'] |
| Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.16941', 'vk6.17182', 'vk6.20550', 'vk6.21950', 'vk6.23337', 'vk6.23630', 'vk6.28005', 'vk6.29471', 'vk6.35385', 'vk6.35804', 'vk6.39410', 'vk6.41601', 'vk6.42858', 'vk6.43135', 'vk6.45986', 'vk6.47660', 'vk6.55092', 'vk6.55343', 'vk6.57432', 'vk6.58600', 'vk6.59490', 'vk6.59780', 'vk6.62099', 'vk6.63075', 'vk6.64941', 'vk6.65147', 'vk6.66964', 'vk6.67824', 'vk6.68230', 'vk6.68371', 'vk6.69576', 'vk6.70272'] |
| 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 | O1O2O3U4O5O6U2U6O4U1U3U5 |
| R3 orbit | {'O1O2O3U4O5O6U2U6O4U1U3U5'} |
| R3 orbit length | 1 |
| Gauss code of -K | O1O2O3U4U1U3O5U6U2O6O4U5 |
| Gauss code of K* | O1O2O3U1U4U2O5U3U6O4O6U5 |
| Gauss code of -K* | O1O2O3U4O5O6U5U1O4U2U6U3 |
| 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 -2 1 0 2 1],[ 2 0 0 2 1 2 1],[ 2 0 0 1 1 2 1],[-1 -2 -1 0 -1 0 0],[ 0 -1 -1 1 0 2 1],[-2 -2 -2 0 -2 0 0],[-1 -1 -1 0 -1 0 0]] |
| Primitive based matrix | [[ 0 2 1 1 0 -2 -2],[-2 0 0 0 -2 -2 -2],[-1 0 0 0 -1 -1 -1],[-1 0 0 0 -1 -1 -2],[ 0 2 1 1 0 -1 -1],[ 2 2 1 1 1 0 0],[ 2 2 1 2 1 0 0]] |
| If based matrix primitive | True |
| Phi of primitive based matrix | [-2,-1,-1,0,2,2,0,0,2,2,2,0,1,1,1,1,1,2,1,1,0] |
| Phi over symmetry | [-2,-2,0,1,1,2,0,1,1,1,2,1,1,2,2,1,1,2,0,0,0] |
| Phi of -K | [-2,-2,0,1,1,2,0,1,1,2,2,1,2,2,2,0,0,0,0,1,1] |
| Phi of K* | [-2,-1,-1,0,2,2,1,1,0,2,2,0,0,1,2,0,2,2,1,1,0] |
| Phi of -K* | [-2,-2,0,1,1,2,0,1,1,1,2,1,1,2,2,1,1,2,0,0,0] |
| Symmetry type of based matrix | c |
| u-polynomial | t^2-2t |
| Normalized Jones-Krushkal polynomial | 3z^2+24z+37 |
| Enhanced Jones-Krushkal polynomial | 3w^3z^2+24w^2z+37w |
| Inner characteristic polynomial | t^6+23t^4+11t^2 |
| Outer characteristic polynomial | t^7+37t^5+32t^3+5t |
| Flat arrow polynomial | -6*K1**2 - 4*K1*K2 + 2*K1 + 3*K2 + 2*K3 + 4 |
| 2-strand cable arrow polynomial | -64*K1**6 + 928*K1**4*K2 - 4032*K1**4 + 32*K1**3*K2*K3 - 1120*K1**3*K3 - 2640*K1**2*K2**2 - 576*K1**2*K2*K4 + 9400*K1**2*K2 - 800*K1**2*K3**2 - 512*K1**2*K4**2 - 6420*K1**2 - 288*K1*K2**2*K3 - 128*K1*K2*K3*K4 + 6048*K1*K2*K3 + 2168*K1*K3*K4 + 456*K1*K4*K5 - 120*K2**4 - 48*K2**2*K3**2 - 48*K2**2*K4**2 + 768*K2**2*K4 - 4956*K2**2 + 72*K2*K3*K5 + 32*K2*K4*K6 - 2384*K3**2 - 958*K4**2 - 92*K5**2 - 4*K6**2 + 5284 |
| Genus of based matrix | 1 |
| Fillings of based matrix | [[{2, 6}, {1, 5}, {3, 4}], [{2, 6}, {4, 5}, {1, 3}], [{3, 6}, {1, 5}, {2, 4}], [{4, 6}, {1, 5}, {2, 3}]] |
| If K is slice | False |