| Min(phi) over symmetries of the knot is: [-3,-1,0,1,1,2,0,0,2,3,3,0,1,1,1,0,1,0,0,1,1] |
| Flat knots (up to 7 crossings) with same phi are :['6.1094'] |
| Arrow polynomial of the knot is: -6*K1**2 - 2*K1*K2 + K1 + 3*K2 + K3 + 4 |
| Flat knots (up to 7 crossings) with same arrow polynomial are :['6.323', '6.380', '6.444', '6.472', '6.523', '6.579', '6.592', '6.595', '6.609', '6.614', '6.620', '6.644', '6.648', '6.669', '6.671', '6.681', '6.693', '6.724', '6.725', '6.757', '6.766', '6.785', '6.786', '6.797', '6.798', '6.816', '6.833', '6.972', '6.978', '6.1056', '6.1064', '6.1066', '6.1087', '6.1094', '6.1273', '6.1277', '6.1282', '6.1295', '6.1300', '6.1313', '6.1344', '6.1353', '6.1354'] |
| Outer characteristic polynomial of the knot is: t^7+50t^5+45t^3+9t |
| Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.1094'] |
| 2-strand cable arrow polynomial of the knot is: -448*K1**6 - 192*K1**4*K2**2 + 1312*K1**4*K2 - 4464*K1**4 + 352*K1**3*K2*K3 + 64*K1**3*K3*K4 - 640*K1**3*K3 + 960*K1**2*K2**3 - 4896*K1**2*K2**2 - 768*K1**2*K2*K4 + 7880*K1**2*K2 - 848*K1**2*K3**2 - 224*K1**2*K3*K5 - 176*K1**2*K4**2 - 3336*K1**2 - 800*K1*K2**2*K3 + 5856*K1*K2*K3 + 1968*K1*K3*K4 + 424*K1*K4*K5 + 24*K1*K5*K6 - 680*K2**4 - 48*K2**2*K3**2 - 8*K2**2*K4**2 + 1128*K2**2*K4 - 3406*K2**2 + 288*K2*K3*K5 + 16*K2*K4*K6 - 2024*K3**2 - 966*K4**2 - 264*K5**2 - 18*K6**2 + 3932 |
| Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.1094'] |
| Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.11256', 'vk6.11334', 'vk6.12521', 'vk6.12632', 'vk6.17607', 'vk6.18923', 'vk6.19001', 'vk6.19363', 'vk6.19656', 'vk6.24061', 'vk6.24153', 'vk6.25517', 'vk6.25618', 'vk6.26135', 'vk6.26553', 'vk6.30930', 'vk6.31053', 'vk6.32112', 'vk6.32231', 'vk6.36410', 'vk6.37656', 'vk6.37705', 'vk6.43509', 'vk6.44788', 'vk6.52006', 'vk6.52101', 'vk6.52928', 'vk6.56504', 'vk6.56675', 'vk6.65390', 'vk6.66126', 'vk6.66162'] |
| 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 | O1O2O3O4U1U4O5U6U3O6U2U5 |
| R3 orbit | {'O1O2O3O4U1U4O5U6U3O6U2U5'} |
| R3 orbit length | 1 |
| Gauss code of -K | O1O2O3O4U5U3O6U2U6O5U1U4 |
| Gauss code of K* | O1O2U3O4O5U4O6O3U1U6U5U2 |
| Gauss code of -K* | O1O2U3O4O3U1O5O6U5U4U2U6 |
| 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 0 1 1 2 -1],[ 3 0 3 2 1 2 2],[ 0 -3 0 1 0 2 -1],[-1 -2 -1 0 0 0 -1],[-1 -1 0 0 0 0 -1],[-2 -2 -2 0 0 0 -2],[ 1 -2 1 1 1 2 0]] |
| Primitive based matrix | [[ 0 2 1 1 0 -1 -3],[-2 0 0 0 -2 -2 -2],[-1 0 0 0 0 -1 -1],[-1 0 0 0 -1 -1 -2],[ 0 2 0 1 0 -1 -3],[ 1 2 1 1 1 0 -2],[ 3 2 1 2 3 2 0]] |
| If based matrix primitive | True |
| Phi of primitive based matrix | [-2,-1,-1,0,1,3,0,0,2,2,2,0,0,1,1,1,1,2,1,3,2] |
| Phi over symmetry | [-3,-1,0,1,1,2,0,0,2,3,3,0,1,1,1,0,1,0,0,1,1] |
| Phi of -K | [-3,-1,0,1,1,2,0,0,2,3,3,0,1,1,1,0,1,0,0,1,1] |
| Phi of K* | [-2,-1,-1,0,1,3,1,1,0,1,3,0,0,1,2,1,1,3,0,0,0] |
| Phi of -K* | [-3,-1,0,1,1,2,2,3,1,2,2,1,1,1,2,0,1,2,0,0,0] |
| Symmetry type of based matrix | c |
| u-polynomial | t^3-t^2-t |
| Normalized Jones-Krushkal polynomial | 3z^2+24z+37 |
| Enhanced Jones-Krushkal polynomial | 3w^3z^2+24w^2z+37w |
| Inner characteristic polynomial | t^6+34t^4+24t^2+4 |
| Outer characteristic polynomial | t^7+50t^5+45t^3+9t |
| Flat arrow polynomial | -6*K1**2 - 2*K1*K2 + K1 + 3*K2 + K3 + 4 |
| 2-strand cable arrow polynomial | -448*K1**6 - 192*K1**4*K2**2 + 1312*K1**4*K2 - 4464*K1**4 + 352*K1**3*K2*K3 + 64*K1**3*K3*K4 - 640*K1**3*K3 + 960*K1**2*K2**3 - 4896*K1**2*K2**2 - 768*K1**2*K2*K4 + 7880*K1**2*K2 - 848*K1**2*K3**2 - 224*K1**2*K3*K5 - 176*K1**2*K4**2 - 3336*K1**2 - 800*K1*K2**2*K3 + 5856*K1*K2*K3 + 1968*K1*K3*K4 + 424*K1*K4*K5 + 24*K1*K5*K6 - 680*K2**4 - 48*K2**2*K3**2 - 8*K2**2*K4**2 + 1128*K2**2*K4 - 3406*K2**2 + 288*K2*K3*K5 + 16*K2*K4*K6 - 2024*K3**2 - 966*K4**2 - 264*K5**2 - 18*K6**2 + 3932 |
| Genus of based matrix | 1 |
| Fillings of based matrix | [[{5, 6}, {2, 4}, {1, 3}], [{5, 6}, {3, 4}, {1, 2}], [{6}, {5}, {2, 4}, {1, 3}], [{6}, {5}, {3, 4}, {1, 2}]] |
| If K is slice | False |