| Min(phi) over symmetries of the knot is: [-2,-1,0,1,1,1,0,1,1,1,3,0,0,1,1,1,0,1,0,-1,-1] |
| Flat knots (up to 7 crossings) with same phi are :['6.1429'] |
| Arrow polynomial of the knot is: -2*K1**2 + K2 + 2 |
| Flat knots (up to 7 crossings) with same arrow polynomial are :['4.6', '4.8', '6.780', '6.804', '6.914', '6.931', '6.946', '6.960', '6.1002', '6.1016', '6.1019', '6.1051', '6.1058', '6.1078', '6.1102', '6.1115', '6.1217', '6.1294', '6.1306', '6.1317', '6.1321', '6.1324', '6.1336', '6.1377', '6.1416', '6.1420', '6.1427', '6.1429', '6.1434', '6.1436', '6.1437', '6.1439', '6.1441', '6.1444', '6.1450', '6.1451', '6.1458', '6.1459', '6.1477', '6.1482', '6.1490', '6.1503', '6.1504', '6.1511', '6.1521', '6.1547', '6.1560', '6.1561', '6.1562', '6.1597', '6.1598', '6.1600', '6.1601', '6.1608', '6.1620', '6.1622', '6.1624', '6.1634', '6.1635', '6.1637', '6.1638', '6.1713', '6.1725', '6.1758', '6.1846', '6.1933', '6.1944', '6.1949', '6.1950', '6.1951'] |
| Outer characteristic polynomial of the knot is: t^7+26t^5+32t^3 |
| Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.1429'] |
| 2-strand cable arrow polynomial of the knot is: 32*K1**4*K2 - 448*K1**4 - 144*K1**2*K2**2 + 664*K1**2*K2 - 188*K1**2 + 104*K1*K2*K3 - 8*K2**4 + 8*K2**2*K4 - 216*K2**2 - 20*K3**2 - 2*K4**2 + 216 |
| Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.1429'] |
| Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.4345', 'vk6.4378', 'vk6.5663', 'vk6.5696', 'vk6.7736', 'vk6.7769', 'vk6.9214', 'vk6.9247', 'vk6.10489', 'vk6.10560', 'vk6.10657', 'vk6.10710', 'vk6.10743', 'vk6.10846', 'vk6.11018', 'vk6.12186', 'vk6.12295', 'vk6.14617', 'vk6.15298', 'vk6.15425', 'vk6.16240', 'vk6.17969', 'vk6.18191', 'vk6.18528', 'vk6.24411', 'vk6.24641', 'vk6.24645', 'vk6.30176', 'vk6.30247', 'vk6.30344', 'vk6.30473', 'vk6.30583', 'vk6.30585', 'vk6.30680', 'vk6.30682', 'vk6.31853', 'vk6.33940', 'vk6.34345', 'vk6.36779', 'vk6.37229', 'vk6.37233', 'vk6.43838', 'vk6.44020', 'vk6.50471', 'vk6.51829', 'vk6.51898', 'vk6.52699', 'vk6.52701', 'vk6.52795', 'vk6.52797', 'vk6.56272', 'vk6.60528', 'vk6.60532', 'vk6.68702', 'vk6.86468', 'vk6.86484'] |
| 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 | O1O2O3U2O4U1O5U4U5O6U3U6 |
| R3 orbit | {'O1O2U3O4O5U2O6U1O3U5U6U4', 'O1O2O3U2O4U1O5U4U5O6U3U6', 'O1O2U1O3O4U5U3O6U4U2O5U6', 'O1O2U3O4U1O5O3U6U4U5O6U2'} |
| R3 orbit length | 4 |
| Gauss code of -K | O1O2O3U4U1O4U5U6O5U3O6U2 |
| Gauss code of K* | O1O2U3O4O3U5U6U4O6U1O5U2 |
| Gauss code of -K* | O1O2U1O3O4U3O5U4O6U2U6U5 |
| Diagrammatic symmetry type | c |
| Flat genus of the diagram | 2 |
| If K is checkerboard colorable | False |
| If K is almost classical | False |
| Based matrix from Gauss code | [[ 0 -2 -1 1 0 1 1],[ 2 0 0 3 1 1 1],[ 1 0 0 1 0 0 1],[-1 -3 -1 0 -1 1 1],[ 0 -1 0 1 0 1 0],[-1 -1 0 -1 -1 0 0],[-1 -1 -1 -1 0 0 0]] |
| Primitive based matrix | [[ 0 1 1 1 0 -1 -2],[-1 0 1 1 -1 -1 -3],[-1 -1 0 0 0 -1 -1],[-1 -1 0 0 -1 0 -1],[ 0 1 0 1 0 0 -1],[ 1 1 1 0 0 0 0],[ 2 3 1 1 1 0 0]] |
| If based matrix primitive | True |
| Phi of primitive based matrix | [-1,-1,-1,0,1,2,-1,-1,1,1,3,0,0,1,1,1,0,1,0,1,0] |
| Phi over symmetry | [-2,-1,0,1,1,1,0,1,1,1,3,0,0,1,1,1,0,1,0,-1,-1] |
| Phi of -K | [-2,-1,0,1,1,1,1,1,0,2,2,1,1,1,2,0,1,0,-1,-1,0] |
| Phi of K* | [-1,-1,-1,0,1,2,-1,0,0,2,2,1,0,1,0,1,1,2,1,1,1] |
| Phi of -K* | [-2,-1,0,1,1,1,0,1,1,1,3,0,0,1,1,1,0,1,0,-1,-1] |
| Symmetry type of based matrix | c |
| u-polynomial | t^2-2t |
| Normalized Jones-Krushkal polynomial | 7z+15 |
| Enhanced Jones-Krushkal polynomial | 7w^2z+15w |
| Inner characteristic polynomial | t^6+18t^4+19t^2 |
| Outer characteristic polynomial | t^7+26t^5+32t^3 |
| Flat arrow polynomial | -2*K1**2 + K2 + 2 |
| 2-strand cable arrow polynomial | 32*K1**4*K2 - 448*K1**4 - 144*K1**2*K2**2 + 664*K1**2*K2 - 188*K1**2 + 104*K1*K2*K3 - 8*K2**4 + 8*K2**2*K4 - 216*K2**2 - 20*K3**2 - 2*K4**2 + 216 |
| Genus of based matrix | 1 |
| Fillings of based matrix | [[{1, 6}, {3, 5}, {2, 4}], [{1, 6}, {5}, {2, 4}, {3}], [{3, 6}, {1, 5}, {2, 4}], [{3, 6}, {5}, {2, 4}, {1}], [{5, 6}, {2, 4}, {1, 3}], [{5, 6}, {2, 4}, {3}, {1}], [{6}, {1, 5}, {2, 4}, {3}], [{6}, {3, 5}, {2, 4}, {1}], [{6}, {5}, {2, 4}, {1, 3}], [{6}, {5}, {2, 4}, {3}, {1}]] |
| If K is slice | False |