| Min(phi) over symmetries of the knot is: [-2,-1,0,0,1,2,0,0,1,2,3,0,0,1,1,0,0,1,1,1,0] |
| Flat knots (up to 7 crossings) with same phi are :['6.1260'] |
| Arrow polynomial of the knot is: -4*K1*K2 + 2*K1 + 2*K3 + 1 |
| Flat knots (up to 7 crossings) with same arrow polynomial are :['6.540', '6.925', '6.1021', '6.1117', '6.1120', '6.1135', '6.1227', '6.1230', '6.1260', '6.1682', '6.1685', '6.1922'] |
| Outer characteristic polynomial of the knot is: t^7+29t^5+31t^3+3t |
| Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.1260'] |
| 2-strand cable arrow polynomial of the knot is: 128*K1**4*K2 - 432*K1**4 + 96*K1**3*K3*K4 - 736*K1**3*K3 - 320*K1**2*K2**2 - 320*K1**2*K2*K4 + 2536*K1**2*K2 - 272*K1**2*K3**2 - 96*K1**2*K3*K5 - 112*K1**2*K4**2 - 2552*K1**2 + 64*K1*K2**3*K3 - 192*K1*K2**2*K3 - 128*K1*K2*K3*K4 + 2184*K1*K2*K3 + 944*K1*K3*K4 + 216*K1*K4*K5 - 64*K2**4 - 64*K2**2*K3**2 - 16*K2**2*K4**2 + 480*K2**2*K4 - 1716*K2**2 + 160*K2*K3*K5 + 32*K2*K4*K6 - 996*K3**2 - 524*K4**2 - 108*K5**2 - 12*K6**2 + 1818 |
| Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.1260'] |
| Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.4668', 'vk6.4955', 'vk6.6130', 'vk6.6617', 'vk6.8143', 'vk6.8545', 'vk6.9521', 'vk6.9876', 'vk6.20369', 'vk6.21710', 'vk6.27677', 'vk6.29221', 'vk6.39117', 'vk6.41371', 'vk6.45865', 'vk6.47526', 'vk6.48700', 'vk6.48903', 'vk6.49464', 'vk6.49683', 'vk6.50724', 'vk6.50923', 'vk6.51203', 'vk6.51404', 'vk6.57230', 'vk6.58455', 'vk6.61844', 'vk6.62979', 'vk6.66845', 'vk6.67713', 'vk6.69481', 'vk6.70203', 'vk6.82020', 'vk6.82758', 'vk6.85361', 'vk6.86695', 'vk6.86939', 'vk6.87042', 'vk6.87591', 'vk6.89472'] |
| 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 | O1O2O3O4U5U1U4O6O5U3U2U6 |
| R3 orbit | {'O1O2O3U4U5U3O5O6U2U1O4U6', 'O1O2O3O4U5U1U4O6O5U3U2U6'} |
| R3 orbit length | 2 |
| Gauss code of -K | O1O2O3O4U5U3U2O6O5U1U4U6 |
| Gauss code of K* | O1O2O3U4U1O5O6O4U2U6U5U3 |
| Gauss code of -K* | O1O2O3U4U1O5O6O4U5U3U2U6 |
| 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 -2 0 0 2 -1 1],[ 2 0 2 1 1 1 1],[ 0 -2 0 0 1 -1 1],[ 0 -1 0 0 1 -1 0],[-2 -1 -1 -1 0 -2 -1],[ 1 -1 1 1 2 0 1],[-1 -1 -1 0 1 -1 0]] |
| Primitive based matrix | [[ 0 2 1 0 0 -1 -2],[-2 0 -1 -1 -1 -2 -1],[-1 1 0 0 -1 -1 -1],[ 0 1 0 0 0 -1 -1],[ 0 1 1 0 0 -1 -2],[ 1 2 1 1 1 0 -1],[ 2 1 1 1 2 1 0]] |
| If based matrix primitive | True |
| Phi of primitive based matrix | [-2,-1,0,0,1,2,1,1,1,2,1,0,1,1,1,0,1,1,1,2,1] |
| Phi over symmetry | [-2,-1,0,0,1,2,0,0,1,2,3,0,0,1,1,0,0,1,1,1,0] |
| Phi of -K | [-2,-1,0,0,1,2,0,0,1,2,3,0,0,1,1,0,0,1,1,1,0] |
| Phi of K* | [-2,-1,0,0,1,2,0,1,1,1,3,0,1,1,2,0,0,0,0,1,0] |
| Phi of -K* | [-2,-1,0,0,1,2,1,1,2,1,1,1,1,1,2,0,0,1,1,1,1] |
| Symmetry type of based matrix | c |
| u-polynomial | 0 |
| Normalized Jones-Krushkal polynomial | 4z^2+17z+19 |
| Enhanced Jones-Krushkal polynomial | 4w^3z^2+17w^2z+19w |
| Inner characteristic polynomial | t^6+19t^4+17t^2 |
| Outer characteristic polynomial | t^7+29t^5+31t^3+3t |
| Flat arrow polynomial | -4*K1*K2 + 2*K1 + 2*K3 + 1 |
| 2-strand cable arrow polynomial | 128*K1**4*K2 - 432*K1**4 + 96*K1**3*K3*K4 - 736*K1**3*K3 - 320*K1**2*K2**2 - 320*K1**2*K2*K4 + 2536*K1**2*K2 - 272*K1**2*K3**2 - 96*K1**2*K3*K5 - 112*K1**2*K4**2 - 2552*K1**2 + 64*K1*K2**3*K3 - 192*K1*K2**2*K3 - 128*K1*K2*K3*K4 + 2184*K1*K2*K3 + 944*K1*K3*K4 + 216*K1*K4*K5 - 64*K2**4 - 64*K2**2*K3**2 - 16*K2**2*K4**2 + 480*K2**2*K4 - 1716*K2**2 + 160*K2*K3*K5 + 32*K2*K4*K6 - 996*K3**2 - 524*K4**2 - 108*K5**2 - 12*K6**2 + 1818 |
| Genus of based matrix | 1 |
| Fillings of based matrix | [[{2, 6}, {3, 5}, {1, 4}], [{3, 6}, {2, 5}, {1, 4}], [{5, 6}, {1, 4}, {2, 3}]] |
| If K is slice | False |