| Min(phi) over symmetries of the knot is: [-2,0,0,0,1,1,0,1,1,1,1,0,1,0,1,0,1,1,0,0,1] |
| Flat knots (up to 7 crossings) with same phi are :['6.1870'] |
| Arrow polynomial of the knot is: -10*K1**2 - 4*K1*K2 + 2*K1 + 5*K2 + 2*K3 + 6 |
| Flat knots (up to 7 crossings) with same arrow polynomial are :['6.425', '6.655', '6.755', '6.769', '6.792', '6.1240', '6.1494', '6.1522', '6.1534', '6.1587', '6.1707', '6.1746', '6.1747', '6.1786', '6.1814', '6.1828', '6.1835', '6.1854', '6.1870'] |
| Outer characteristic polynomial of the knot is: t^7+15t^5+31t^3+4t |
| Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.1870'] |
| 2-strand cable arrow polynomial of the knot is: -64*K1**6 + 384*K1**4*K2 - 2112*K1**4 + 32*K1**3*K2*K3 - 384*K1**3*K3 - 2928*K1**2*K2**2 - 96*K1**2*K2*K4 + 6936*K1**2*K2 - 384*K1**2*K3**2 - 48*K1**2*K4**2 - 4728*K1**2 - 672*K1*K2**2*K3 - 64*K1*K2*K3*K4 + 4936*K1*K2*K3 + 928*K1*K3*K4 + 80*K1*K4*K5 - 440*K2**4 - 320*K2**2*K3**2 - 48*K2**2*K4**2 + 768*K2**2*K4 - 3612*K2**2 + 272*K2*K3*K5 + 32*K2*K4*K6 - 1700*K3**2 - 446*K4**2 - 68*K5**2 - 4*K6**2 + 3748 |
| Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.1870'] |
| Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.16947', 'vk6.17188', 'vk6.20541', 'vk6.21942', 'vk6.23347', 'vk6.23640', 'vk6.27999', 'vk6.29466', 'vk6.35387', 'vk6.35806', 'vk6.39399', 'vk6.41592', 'vk6.42864', 'vk6.43141', 'vk6.45979', 'vk6.47655', 'vk6.55110', 'vk6.55369', 'vk6.57405', 'vk6.58580', 'vk6.59512', 'vk6.59810', 'vk6.62076', 'vk6.63058', 'vk6.64955', 'vk6.65161', 'vk6.66945', 'vk6.67806', 'vk6.68248', 'vk6.68389', 'vk6.69560', 'vk6.70257'] |
| 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 | O1O2O3U4U1O5U2O6O4U6U5U3 |
| R3 orbit | {'O1O2O3U4U1O5U2O6O4U6U5U3'} |
| R3 orbit length | 1 |
| Gauss code of -K | O1O2O3U1U4U5O6O5U2O4U3U6 |
| Gauss code of K* | O1O2O3U4U5U3O6O4U2O5U1U6 |
| Gauss code of -K* | O1O2O3U4U3O5U2O6O4U1U5U6 |
| 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 -1 0 2 0 0 -1],[ 1 0 1 1 0 0 -1],[ 0 -1 0 1 0 0 -1],[-2 -1 -1 0 0 -1 -1],[ 0 0 0 0 0 -1 -1],[ 0 0 0 1 1 0 0],[ 1 1 1 1 1 0 0]] |
| Primitive based matrix | [[ 0 2 0 0 0 -1 -1],[-2 0 0 -1 -1 -1 -1],[ 0 0 0 0 -1 0 -1],[ 0 1 0 0 0 -1 -1],[ 0 1 1 0 0 0 0],[ 1 1 0 1 0 0 -1],[ 1 1 1 1 0 1 0]] |
| If based matrix primitive | True |
| Phi of primitive based matrix | [-2,0,0,0,1,1,0,1,1,1,1,0,1,0,1,0,1,1,0,0,1] |
| Phi over symmetry | [-2,0,0,0,1,1,0,1,1,1,1,0,1,0,1,0,1,1,0,0,1] |
| Phi of -K | [-1,-1,0,0,0,2,-1,0,0,1,2,0,1,1,2,0,0,1,1,2,1] |
| Phi of K* | [-2,0,0,0,1,1,1,1,2,2,2,0,0,0,0,1,1,1,0,1,1] |
| Phi of -K* | [-1,-1,0,0,0,2,-1,0,0,1,1,0,1,1,1,1,0,1,0,0,1] |
| Symmetry type of based matrix | c |
| u-polynomial | -t^2+2t |
| Normalized Jones-Krushkal polynomial | z^2+18z+33 |
| Enhanced Jones-Krushkal polynomial | w^3z^2+18w^2z+33w |
| Inner characteristic polynomial | t^6+9t^4+12t^2 |
| Outer characteristic polynomial | t^7+15t^5+31t^3+4t |
| Flat arrow polynomial | -10*K1**2 - 4*K1*K2 + 2*K1 + 5*K2 + 2*K3 + 6 |
| 2-strand cable arrow polynomial | -64*K1**6 + 384*K1**4*K2 - 2112*K1**4 + 32*K1**3*K2*K3 - 384*K1**3*K3 - 2928*K1**2*K2**2 - 96*K1**2*K2*K4 + 6936*K1**2*K2 - 384*K1**2*K3**2 - 48*K1**2*K4**2 - 4728*K1**2 - 672*K1*K2**2*K3 - 64*K1*K2*K3*K4 + 4936*K1*K2*K3 + 928*K1*K3*K4 + 80*K1*K4*K5 - 440*K2**4 - 320*K2**2*K3**2 - 48*K2**2*K4**2 + 768*K2**2*K4 - 3612*K2**2 + 272*K2*K3*K5 + 32*K2*K4*K6 - 1700*K3**2 - 446*K4**2 - 68*K5**2 - 4*K6**2 + 3748 |
| Genus of based matrix | 1 |
| Fillings of based matrix | [[{1, 6}, {4, 5}, {2, 3}], [{2, 6}, {1, 5}, {3, 4}], [{2, 6}, {4, 5}, {1, 3}], [{3, 6}, {4, 5}, {1, 2}]] |
| If K is slice | False |