| Min(phi) over symmetries of the knot is: [-3,-2,0,2,3,0,1,2,4,1,1,2,1,1,0] |
| Flat knots (up to 7 crossings) with same phi are :['6.572', '7.10854'] |
| 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^6+69t^4+34t^2 |
| Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.572'] |
| 2-strand cable arrow polynomial of the knot is: -224*K1**2*K2**2 + 768*K1**2*K2 - 640*K1**2*K3**2 - 2008*K1**2 + 64*K1*K2*K3**3 + 2704*K1*K2*K3 + 752*K1*K3*K4 + 16*K1*K4*K5 - 16*K2**4 - 128*K2**2*K3**2 - 16*K2**2*K4**2 + 240*K2**2*K4 - 1676*K2**2 + 64*K2*K3*K5 + 16*K2*K4*K6 - 32*K3**4 - 1320*K3**2 - 348*K4**2 - 16*K5**2 - 4*K6**2 + 1802 |
| Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.572'] |
| Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.81583', 'vk6.81665', 'vk6.81906', 'vk6.82103', 'vk6.82269', 'vk6.82345', 'vk6.82625', 'vk6.82871', 'vk6.83158', 'vk6.83377', 'vk6.84155', 'vk6.84658', 'vk6.84973', 'vk6.85969', 'vk6.86181', 'vk6.86434', 'vk6.88129', 'vk6.89053', 'vk6.89721', 'vk6.90041'] |
| The R3 orbit of minmal crossing diagrams contains: |
| The diagrammatic symmetry type of this knot is -. |
| The reverse -K is |
| The 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 | O1O2O3O4U1O5U2O6U4U3U5U6 |
| R3 orbit | {'O1O2O3O4U1O5U2O6U4U3U5U6'} |
| R3 orbit length | 1 |
| Gauss code of -K | O1O2O3O4U5U6U2U1O5U3O6U4 |
| Gauss code of K* | O1O2O3O4U5U6U2U1O5U3O6U4 |
| Gauss code of -K* | Same |
| Diagrammatic symmetry type | - |
| Flat genus of the diagram | 2 |
| If K is checkerboard colorable | False |
| If K is almost classical | False |
| Based matrix from Gauss code | [[ 0 -3 -2 0 0 2 3],[ 3 0 1 3 2 3 2],[ 2 -1 0 2 1 3 3],[ 0 -3 -2 0 0 2 3],[ 0 -2 -1 0 0 1 2],[-2 -3 -3 -2 -1 0 1],[-3 -2 -3 -3 -2 -1 0]] |
| Primitive based matrix | [[ 0 3 2 0 -2 -3],[-3 0 -1 -2 -3 -2],[-2 1 0 -1 -3 -3],[ 0 2 1 0 -1 -2],[ 2 3 3 1 0 -1],[ 3 2 3 2 1 0]] |
| If based matrix primitive | False |
| Phi of primitive based matrix | [-3,-2,0,2,3,1,2,3,2,1,3,3,1,2,1] |
| Phi over symmetry | [-3,-2,0,2,3,0,1,2,4,1,1,2,1,1,0] |
| Phi of -K | [-3,-2,0,2,3,0,1,2,4,1,1,2,1,1,0] |
| Phi of K* | [-3,-2,0,2,3,0,1,2,4,1,1,2,1,1,0] |
| Phi of -K* | [-3,-2,0,2,3,1,2,3,2,1,3,3,1,2,1] |
| Symmetry type of based matrix | - |
| u-polynomial | 0 |
| Normalized Jones-Krushkal polynomial | 6z+13 |
| Enhanced Jones-Krushkal polynomial | 4w^4z-12w^3z+14w^2z+13w |
| Inner characteristic polynomial | t^5+43t^3+20t |
| Outer characteristic polynomial | t^6+69t^4+34t^2 |
| Flat arrow polynomial | -4*K1**2 - 4*K1*K2 + 2*K1 + 2*K2 + 2*K3 + 3 |
| 2-strand cable arrow polynomial | -224*K1**2*K2**2 + 768*K1**2*K2 - 640*K1**2*K3**2 - 2008*K1**2 + 64*K1*K2*K3**3 + 2704*K1*K2*K3 + 752*K1*K3*K4 + 16*K1*K4*K5 - 16*K2**4 - 128*K2**2*K3**2 - 16*K2**2*K4**2 + 240*K2**2*K4 - 1676*K2**2 + 64*K2*K3*K5 + 16*K2*K4*K6 - 32*K3**4 - 1320*K3**2 - 348*K4**2 - 16*K5**2 - 4*K6**2 + 1802 |
| Genus of based matrix | 0 |
| Fillings of based matrix | [[{1, 6}, {2, 5}, {3, 4}], [{1, 6}, {2, 5}, {4}, {3}]] |
| If K is slice | True |