| Min(phi) over symmetries of the knot is: [-2,-2,1,1,1,1,-1,1,2,2,2,0,0,1,2,-1,-1,-1,0,0,0] |
| Flat knots (up to 7 crossings) with same phi are :['6.564'] |
| Arrow polynomial of the knot is: -4*K1**2 - 4*K1*K2 + 2*K1 + 2*K2 + 2*K3 + 3 |
| Flat knots (up to 7 crossings) with same arrow polynomial are :['6.65', '6.137', '6.201', '6.203', '6.214', '6.310', '6.314', '6.332', '6.385', '6.386', '6.401', '6.516', '6.564', '6.571', '6.572', '6.578', '6.621', '6.626', '6.716', '6.773', '6.807', '6.814', '6.821', '6.940', '6.966', '6.1036', '6.1071', '6.1108', '6.1111', '6.1131', '6.1188', '6.1203', '6.1206', '6.1220', '6.1340', '6.1387', '6.1548', '6.1663', '6.1680', '6.1693', '6.1831', '6.1932'] |
| Outer characteristic polynomial of the knot is: t^7+46t^5+46t^3+6t |
| Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.564'] |
| 2-strand cable arrow polynomial of the knot is: -432*K1**4 + 192*K1**3*K2*K3 - 1616*K1**2*K2**2 - 800*K1**2*K2*K4 + 2480*K1**2*K2 - 208*K1**2*K3**2 - 128*K1**2*K4**2 - 2592*K1**2 - 128*K1*K2**2*K3 - 256*K1*K2**2*K5 - 96*K1*K2*K3*K4 + 3336*K1*K2*K3 + 1136*K1*K3*K4 + 360*K1*K4*K5 - 208*K2**4 - 16*K2**2*K3**2 - 48*K2**2*K4**2 + 936*K2**2*K4 - 2284*K2**2 + 376*K2*K3*K5 + 32*K2*K4*K6 - 1364*K3**2 - 744*K4**2 - 244*K5**2 - 4*K6**2 + 2318 |
| Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.564'] |
| Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.4710', 'vk6.5021', 'vk6.6228', 'vk6.6685', 'vk6.8207', 'vk6.8638', 'vk6.9583', 'vk6.9916', 'vk6.17401', 'vk6.20936', 'vk6.21086', 'vk6.22347', 'vk6.22514', 'vk6.23573', 'vk6.23910', 'vk6.28415', 'vk6.36176', 'vk6.40093', 'vk6.40328', 'vk6.42139', 'vk6.43393', 'vk6.46615', 'vk6.46794', 'vk6.48049', 'vk6.48744', 'vk6.49755', 'vk6.50752', 'vk6.51440', 'vk6.57738', 'vk6.58943', 'vk6.65298', 'vk6.69778'] |
| 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 | O1O2O3O4O5U4U3U2O6U5U1U6 |
| R3 orbit | {'O1O2O3O4O5U4U3U2O6U5U1U6'} |
| R3 orbit length | 1 |
| Gauss code of -K | O1O2O3O4O5U6U5U1O6U4U3U2 |
| Gauss code of K* | O1O2O3U4O5O6O4U6U3U2U1U5 |
| Gauss code of -K* | O1O2O3U1O4O5O6U3U6U5U4U2 |
| 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 -1 -1 -1 2 2],[ 1 0 -1 -1 -1 3 2],[ 1 1 0 0 0 3 1],[ 1 1 0 0 0 2 1],[ 1 1 0 0 0 1 1],[-2 -3 -3 -2 -1 0 1],[-2 -2 -1 -1 -1 -1 0]] |
| Primitive based matrix | [[ 0 2 2 -1 -1 -1 -1],[-2 0 1 -1 -2 -3 -3],[-2 -1 0 -1 -1 -1 -2],[ 1 1 1 0 0 0 1],[ 1 2 1 0 0 0 1],[ 1 3 1 0 0 0 1],[ 1 3 2 -1 -1 -1 0]] |
| If based matrix primitive | True |
| Phi of primitive based matrix | [-2,-2,1,1,1,1,-1,1,2,3,3,1,1,1,2,0,0,-1,0,-1,-1] |
| Phi over symmetry | [-2,-2,1,1,1,1,-1,1,2,2,2,0,0,1,2,-1,-1,-1,0,0,0] |
| Phi of -K | [-1,-1,-1,-1,2,2,-1,0,0,0,2,1,1,0,1,0,1,2,2,2,-1] |
| Phi of K* | [-2,-2,1,1,1,1,-1,1,2,2,2,0,0,1,2,-1,-1,-1,0,0,0] |
| Phi of -K* | [-1,-1,-1,-1,2,2,-1,-1,-1,2,3,0,0,1,1,0,1,2,1,3,-1] |
| Symmetry type of based matrix | c |
| u-polynomial | -2t^2+4t |
| Normalized Jones-Krushkal polynomial | 5z+11 |
| Enhanced Jones-Krushkal polynomial | -4w^4z^2+4w^3z^2-12w^3z+17w^2z+11w |
| Inner characteristic polynomial | t^6+34t^4+20t^2 |
| Outer characteristic polynomial | t^7+46t^5+46t^3+6t |
| Flat arrow polynomial | -4*K1**2 - 4*K1*K2 + 2*K1 + 2*K2 + 2*K3 + 3 |
| 2-strand cable arrow polynomial | -432*K1**4 + 192*K1**3*K2*K3 - 1616*K1**2*K2**2 - 800*K1**2*K2*K4 + 2480*K1**2*K2 - 208*K1**2*K3**2 - 128*K1**2*K4**2 - 2592*K1**2 - 128*K1*K2**2*K3 - 256*K1*K2**2*K5 - 96*K1*K2*K3*K4 + 3336*K1*K2*K3 + 1136*K1*K3*K4 + 360*K1*K4*K5 - 208*K2**4 - 16*K2**2*K3**2 - 48*K2**2*K4**2 + 936*K2**2*K4 - 2284*K2**2 + 376*K2*K3*K5 + 32*K2*K4*K6 - 1364*K3**2 - 744*K4**2 - 244*K5**2 - 4*K6**2 + 2318 |
| Genus of based matrix | 1 |
| Fillings of based matrix | [[{1, 6}, {3, 5}, {2, 4}], [{1, 6}, {5}, {2, 4}, {3}], [{4, 6}, {2, 5}, {1, 3}], [{5, 6}, {3, 4}, {1, 2}]] |
| If K is slice | False |