| Min(phi) over symmetries of the knot is: [-2,-1,0,1,1,1,0,1,1,1,1,1,1,1,1,1,1,1,-1,0,0] |
| Flat knots (up to 7 crossings) with same phi are :['6.1679', '7.37718'] |
| 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+20t^5+18t^3+3t |
| Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.1679'] |
| 2-strand cable arrow polynomial of the knot is: -256*K1**6 - 256*K1**4*K2**2 + 928*K1**4*K2 - 1984*K1**4 + 384*K1**3*K2*K3 - 352*K1**3*K3 - 1696*K1**2*K2**2 - 128*K1**2*K2*K4 + 3656*K1**2*K2 - 128*K1**2*K3**2 - 1468*K1**2 - 192*K1*K2**2*K3 - 64*K1*K2*K3*K4 + 1896*K1*K2*K3 + 192*K1*K3*K4 + 16*K1*K4*K5 - 168*K2**4 - 144*K2**2*K3**2 - 48*K2**2*K4**2 + 344*K2**2*K4 - 1532*K2**2 + 144*K2*K3*K5 + 32*K2*K4*K6 - 520*K3**2 - 130*K4**2 - 28*K5**2 - 4*K6**2 + 1504 |
| Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.1679'] |
| Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.11044', 'vk6.11124', 'vk6.11558', 'vk6.11899', 'vk6.12206', 'vk6.12315', 'vk6.13213', 'vk6.19229', 'vk6.19324', 'vk6.19524', 'vk6.19619', 'vk6.22390', 'vk6.22708', 'vk6.22811', 'vk6.26039', 'vk6.26092', 'vk6.26516', 'vk6.28428', 'vk6.30621', 'vk6.30718', 'vk6.31339', 'vk6.31359', 'vk6.31752', 'vk6.31925', 'vk6.32521', 'vk6.32922', 'vk6.34764', 'vk6.38111', 'vk6.40143', 'vk6.40159', 'vk6.42379', 'vk6.44632', 'vk6.44754', 'vk6.46668', 'vk6.52346', 'vk6.52607', 'vk6.52815', 'vk6.56623', 'vk6.64721', 'vk6.66288'] |
| 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 | O1O2O3U2O4U5U3U1O6O5U6U4 |
| R3 orbit | {'O1O2U1O3O4U5U2U3O6O5U6U4', 'O1O2O3U2O4U5U3U1O6O5U6U4'} |
| R3 orbit length | 2 |
| Gauss code of -K | O1O2O3U4U5O6O5U3U1U6O4U2 |
| Gauss code of K* | O1O2O3U4U1O4O5U3U6U2O6U5 |
| Gauss code of -K* | O1O2O3U4O5U2U5U1O4O6U3U6 |
| 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 0 -1 1 2 -1 -1],[ 0 0 -1 1 1 -1 -1],[ 1 1 0 1 1 0 0],[-1 -1 -1 0 0 -1 -1],[-2 -1 -1 0 0 -1 -1],[ 1 1 0 1 1 0 -1],[ 1 1 0 1 1 1 0]] |
| Primitive based matrix | [[ 0 2 1 0 -1 -1 -1],[-2 0 0 -1 -1 -1 -1],[-1 0 0 -1 -1 -1 -1],[ 0 1 1 0 -1 -1 -1],[ 1 1 1 1 0 1 0],[ 1 1 1 1 -1 0 0],[ 1 1 1 1 0 0 0]] |
| If based matrix primitive | True |
| Phi of primitive based matrix | [-2,-1,0,1,1,1,0,1,1,1,1,1,1,1,1,1,1,1,-1,0,0] |
| Phi over symmetry | [-2,-1,0,1,1,1,0,1,1,1,1,1,1,1,1,1,1,1,-1,0,0] |
| Phi of -K | [-1,-1,-1,0,1,2,-1,0,0,1,2,0,0,1,2,0,1,2,0,1,1] |
| Phi of K* | [-2,-1,0,1,1,1,1,1,2,2,2,0,1,1,1,0,0,0,-1,0,0] |
| Phi of -K* | [-1,-1,-1,0,1,2,-1,0,1,1,1,0,1,1,1,1,1,1,1,1,0] |
| Symmetry type of based matrix | c |
| u-polynomial | -t^2+2t |
| Normalized Jones-Krushkal polynomial | z^2+14z+25 |
| Enhanced Jones-Krushkal polynomial | w^3z^2+14w^2z+25w |
| Inner characteristic polynomial | t^6+12t^4+5t^2 |
| Outer characteristic polynomial | t^7+20t^5+18t^3+3t |
| Flat arrow polynomial | -6*K1**2 - 4*K1*K2 + 2*K1 + 3*K2 + 2*K3 + 4 |
| 2-strand cable arrow polynomial | -256*K1**6 - 256*K1**4*K2**2 + 928*K1**4*K2 - 1984*K1**4 + 384*K1**3*K2*K3 - 352*K1**3*K3 - 1696*K1**2*K2**2 - 128*K1**2*K2*K4 + 3656*K1**2*K2 - 128*K1**2*K3**2 - 1468*K1**2 - 192*K1*K2**2*K3 - 64*K1*K2*K3*K4 + 1896*K1*K2*K3 + 192*K1*K3*K4 + 16*K1*K4*K5 - 168*K2**4 - 144*K2**2*K3**2 - 48*K2**2*K4**2 + 344*K2**2*K4 - 1532*K2**2 + 144*K2*K3*K5 + 32*K2*K4*K6 - 520*K3**2 - 130*K4**2 - 28*K5**2 - 4*K6**2 + 1504 |
| Genus of based matrix | 1 |
| Fillings of based matrix | [[{3, 6}, {1, 5}, {2, 4}], [{3, 6}, {2, 5}, {1, 4}], [{3, 6}, {4, 5}, {1, 2}]] |
| If K is slice | False |