| Min(phi) over symmetries of the knot is: [-2,-1,0,0,1,2,0,1,2,1,2,1,1,1,2,0,1,2,0,1,0] |
| Flat knots (up to 7 crossings) with same phi are :['6.1411', '7.35252'] |
| Arrow polynomial of the knot is: -12*K1**2 + 6*K2 + 7 |
| Flat knots (up to 7 crossings) with same arrow polynomial are :['6.612', '6.1246', '6.1402', '6.1410', '6.1411', '6.1468', '6.1617', '6.1666', '6.1667', '6.1815', '6.1904', '6.1994', '6.1995', '6.1996', '6.2001', '6.2014', '6.2015', '6.2016', '6.2017', '6.2020', '6.2022'] |
| Outer characteristic polynomial of the knot is: t^7+25t^5+30t^3+4t |
| Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.1411'] |
| 2-strand cable arrow polynomial of the knot is: 224*K1**4*K2 - 2528*K1**4 + 224*K1**3*K2*K3 - 608*K1**3*K3 + 32*K1**2*K2**3 - 3312*K1**2*K2**2 - 192*K1**2*K2*K4 + 7888*K1**2*K2 - 352*K1**2*K3**2 - 5060*K1**2 - 384*K1*K2**2*K3 + 5056*K1*K2*K3 + 624*K1*K3*K4 - 192*K2**4 + 384*K2**2*K4 - 3784*K2**2 - 1612*K3**2 - 256*K4**2 + 3846 |
| Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.1411'] |
| Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.73302', 'vk6.73310', 'vk6.73443', 'vk6.73451', 'vk6.74080', 'vk6.74096', 'vk6.74651', 'vk6.74667', 'vk6.75443', 'vk6.75451', 'vk6.76114', 'vk6.76130', 'vk6.78183', 'vk6.78191', 'vk6.78413', 'vk6.78421', 'vk6.79082', 'vk6.79098', 'vk6.80004', 'vk6.80012', 'vk6.80155', 'vk6.80163', 'vk6.80586', 'vk6.80602', 'vk6.83798', 'vk6.83800', 'vk6.85115', 'vk6.85119', 'vk6.86609', 'vk6.86613', 'vk6.87390', 'vk6.87398'] |
| 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 | O1O2O3U4O5U1O6U2O4U6U5U3 |
| R3 orbit | {'O1O2O3U4O5U1O6U2O4U6U5U3'} |
| R3 orbit length | 1 |
| Gauss code of -K | O1O2O3U1U4U5O6U2O5U3O4U6 |
| Gauss code of K* | O1O2O3U4U5U3O6U2O4U1O5U6 |
| Gauss code of -K* | O1O2O3U4O5U3O6U2O4U1U5U6 |
| 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 -1 2 0 1 0],[ 2 0 1 2 1 1 0],[ 1 -1 0 2 1 1 0],[-2 -2 -2 0 0 -1 -1],[ 0 -1 -1 0 0 0 0],[-1 -1 -1 1 0 0 0],[ 0 0 0 1 0 0 0]] |
| Primitive based matrix | [[ 0 2 1 0 0 -1 -2],[-2 0 -1 0 -1 -2 -2],[-1 1 0 0 0 -1 -1],[ 0 0 0 0 0 -1 -1],[ 0 1 0 0 0 0 0],[ 1 2 1 1 0 0 -1],[ 2 2 1 1 0 1 0]] |
| If based matrix primitive | True |
| Phi of primitive based matrix | [-2,-1,0,0,1,2,1,0,1,2,2,0,0,1,1,0,1,1,0,0,1] |
| Phi over symmetry | [-2,-1,0,0,1,2,0,1,2,1,2,1,1,1,2,0,1,2,0,1,0] |
| Phi of -K | [-2,-1,0,0,1,2,0,1,2,2,2,0,1,1,1,0,1,2,1,1,0] |
| Phi of K* | [-2,-1,0,0,1,2,0,1,2,1,2,1,1,1,2,0,1,2,0,1,0] |
| Phi of -K* | [-2,-1,0,0,1,2,1,0,1,1,2,0,1,1,2,0,0,1,0,0,1] |
| Symmetry type of based matrix | c |
| u-polynomial | 0 |
| Normalized Jones-Krushkal polynomial | 17z+35 |
| Enhanced Jones-Krushkal polynomial | 17w^2z+35w |
| Inner characteristic polynomial | t^6+15t^4+8t^2 |
| Outer characteristic polynomial | t^7+25t^5+30t^3+4t |
| Flat arrow polynomial | -12*K1**2 + 6*K2 + 7 |
| 2-strand cable arrow polynomial | 224*K1**4*K2 - 2528*K1**4 + 224*K1**3*K2*K3 - 608*K1**3*K3 + 32*K1**2*K2**3 - 3312*K1**2*K2**2 - 192*K1**2*K2*K4 + 7888*K1**2*K2 - 352*K1**2*K3**2 - 5060*K1**2 - 384*K1*K2**2*K3 + 5056*K1*K2*K3 + 624*K1*K3*K4 - 192*K2**4 + 384*K2**2*K4 - 3784*K2**2 - 1612*K3**2 - 256*K4**2 + 3846 |
| Genus of based matrix | 1 |
| Fillings of based matrix | [[{1, 6}, {4, 5}, {2, 3}], [{2, 6}, {1, 5}, {3, 4}], [{4, 6}, {2, 5}, {1, 3}]] |
| If K is slice | False |