| Min(phi) over symmetries of the knot is: [-3,-2,0,1,1,3,0,2,1,2,4,1,1,1,2,1,1,3,-1,-1,1] |
| Flat knots (up to 7 crossings) with same phi are :['6.428'] |
| 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+72t^5+85t^3+4t |
| Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.425', '6.428'] |
| 2-strand cable arrow polynomial of the knot is: -64*K1**6 + 224*K1**4*K2 - 1376*K1**4 + 96*K1**3*K2*K3 - 1248*K1**3*K3 - 1056*K1**2*K2**2 + 96*K1**2*K2*K3**2 - 288*K1**2*K2*K4 + 5696*K1**2*K2 - 896*K1**2*K3**2 - 96*K1**2*K3*K5 - 176*K1**2*K4**2 - 96*K1**2*K4*K6 - 5268*K1**2 - 352*K1*K2**2*K3 - 224*K1*K2*K3*K4 + 5056*K1*K2*K3 - 32*K1*K3**2*K5 + 1664*K1*K3*K4 + 464*K1*K4*K5 + 88*K1*K5*K6 - 56*K2**4 - 160*K2**2*K3**2 - 48*K2**2*K4**2 + 480*K2**2*K4 - 3556*K2**2 - 32*K2*K3**2*K4 + 320*K2*K3*K5 + 128*K2*K4*K6 + 56*K3**2*K6 - 2168*K3**2 - 758*K4**2 - 228*K5**2 - 84*K6**2 + 3892 |
| Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.428'] |
| Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.19998', 'vk6.20076', 'vk6.21270', 'vk6.21358', 'vk6.27049', 'vk6.27141', 'vk6.28754', 'vk6.28830', 'vk6.38446', 'vk6.38542', 'vk6.40635', 'vk6.40739', 'vk6.45330', 'vk6.45442', 'vk6.47099', 'vk6.47184', 'vk6.56813', 'vk6.56897', 'vk6.57947', 'vk6.58035', 'vk6.61331', 'vk6.61427', 'vk6.62507', 'vk6.62584', 'vk6.66533', 'vk6.66605', 'vk6.67322', 'vk6.67396', 'vk6.69179', 'vk6.69257', 'vk6.69930', 'vk6.69998'] |
| 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 | O1O2O3O4O5U6U1O6U4U2U5U3 |
| R3 orbit | {'O1O2O3O4O5U6U1O6U4U2U5U3'} |
| R3 orbit length | 1 |
| Gauss code of -K | O1O2O3O4O5U3U1U4U2O6U5U6 |
| Gauss code of K* | O1O2O3O4U5U2U4U1U3O6O5U6 |
| Gauss code of -K* | O1O2O3O4U5O6O5U2U4U1U3U6 |
| 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 2 0 3 -1],[ 3 0 1 3 0 2 3],[ 1 -1 0 2 0 2 1],[-2 -3 -2 0 -1 1 -2],[ 0 0 0 1 0 1 0],[-3 -2 -2 -1 -1 0 -3],[ 1 -3 -1 2 0 3 0]] |
| Primitive based matrix | [[ 0 3 2 0 -1 -1 -3],[-3 0 -1 -1 -2 -3 -2],[-2 1 0 -1 -2 -2 -3],[ 0 1 1 0 0 0 0],[ 1 2 2 0 0 1 -1],[ 1 3 2 0 -1 0 -3],[ 3 2 3 0 1 3 0]] |
| If based matrix primitive | True |
| Phi of primitive based matrix | [-3,-2,0,1,1,3,1,1,2,3,2,1,2,2,3,0,0,0,-1,1,3] |
| Phi over symmetry | [-3,-2,0,1,1,3,0,2,1,2,4,1,1,1,2,1,1,3,-1,-1,1] |
| Phi of -K | [-3,-1,-1,0,2,3,-1,1,3,2,4,1,1,1,1,1,1,2,1,2,0] |
| Phi of K* | [-3,-2,0,1,1,3,0,2,1,2,4,1,1,1,2,1,1,3,-1,-1,1] |
| Phi of -K* | [-3,-1,-1,0,2,3,1,3,0,3,2,1,0,2,2,0,2,3,1,1,1] |
| Symmetry type of based matrix | c |
| u-polynomial | -t^2+2t |
| Normalized Jones-Krushkal polynomial | 17z+35 |
| Enhanced Jones-Krushkal polynomial | 17w^2z+35w |
| Inner characteristic polynomial | t^6+48t^4+32t^2 |
| Outer characteristic polynomial | t^7+72t^5+85t^3+4t |
| Flat arrow polynomial | -6*K1**2 - 4*K1*K2 + 2*K1 + 3*K2 + 2*K3 + 4 |
| 2-strand cable arrow polynomial | -64*K1**6 + 224*K1**4*K2 - 1376*K1**4 + 96*K1**3*K2*K3 - 1248*K1**3*K3 - 1056*K1**2*K2**2 + 96*K1**2*K2*K3**2 - 288*K1**2*K2*K4 + 5696*K1**2*K2 - 896*K1**2*K3**2 - 96*K1**2*K3*K5 - 176*K1**2*K4**2 - 96*K1**2*K4*K6 - 5268*K1**2 - 352*K1*K2**2*K3 - 224*K1*K2*K3*K4 + 5056*K1*K2*K3 - 32*K1*K3**2*K5 + 1664*K1*K3*K4 + 464*K1*K4*K5 + 88*K1*K5*K6 - 56*K2**4 - 160*K2**2*K3**2 - 48*K2**2*K4**2 + 480*K2**2*K4 - 3556*K2**2 - 32*K2*K3**2*K4 + 320*K2*K3*K5 + 128*K2*K4*K6 + 56*K3**2*K6 - 2168*K3**2 - 758*K4**2 - 228*K5**2 - 84*K6**2 + 3892 |
| Genus of based matrix | 1 |
| Fillings of based matrix | [[{1, 6}, {2, 5}, {3, 4}], [{2, 6}, {1, 5}, {3, 4}], [{3, 6}, {1, 5}, {2, 4}], [{4, 6}, {1, 5}, {2, 3}]] |
| If K is slice | False |