| Min(phi) over symmetries of the knot is: [-2,-1,0,1,1,1,0,1,0,1,2,0,1,0,1,1,1,0,-1,-1,0] |
| Flat knots (up to 7 crossings) with same phi are :['6.1574'] |
| Arrow polynomial of the knot is: -2*K1**2 - 4*K1*K2 + 2*K1 + K2 + 2*K3 + 2 |
| Flat knots (up to 7 crossings) with same arrow polynomial are :['6.120', '6.213', '6.216', '6.320', '6.322', '6.615', '6.617', '6.891', '6.951', '6.955', '6.1001', '6.1012', '6.1022', '6.1043', '6.1047', '6.1063', '6.1074', '6.1249', '6.1544', '6.1546', '6.1555', '6.1573', '6.1574', '6.1585', '6.1756', '6.1757', '6.1762', '6.1802', '6.1803', '6.1824', '6.1881', '6.1935'] |
| Outer characteristic polynomial of the knot is: t^7+20t^5+40t^3+13t |
| Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.1574'] |
| 2-strand cable arrow polynomial of the knot is: 384*K1**4*K2 - 3184*K1**4 + 896*K1**3*K2*K3 + 32*K1**3*K3*K4 - 992*K1**3*K3 - 3888*K1**2*K2**2 - 1408*K1**2*K2*K4 + 6552*K1**2*K2 - 1232*K1**2*K3**2 - 176*K1**2*K4**2 - 3564*K1**2 + 64*K1*K2**3*K3 - 192*K1*K2**2*K3 - 64*K1*K2**2*K5 - 96*K1*K2*K3*K4 + 6760*K1*K2*K3 + 2176*K1*K3*K4 + 168*K1*K4*K5 - 40*K2**4 - 96*K2**2*K3**2 - 48*K2**2*K4**2 + 504*K2**2*K4 - 3108*K2**2 + 96*K2*K3*K5 + 32*K2*K4*K6 - 2200*K3**2 - 702*K4**2 - 36*K5**2 - 4*K6**2 + 3364 |
| Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.1574'] |
| Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.16992', 'vk6.17234', 'vk6.20212', 'vk6.21500', 'vk6.23395', 'vk6.23702', 'vk6.27404', 'vk6.29022', 'vk6.35459', 'vk6.35900', 'vk6.38817', 'vk6.41000', 'vk6.42892', 'vk6.43192', 'vk6.45574', 'vk6.47349', 'vk6.55161', 'vk6.55407', 'vk6.57048', 'vk6.58153', 'vk6.59538', 'vk6.59880', 'vk6.61552', 'vk6.62730', 'vk6.64971', 'vk6.65177', 'vk6.66665', 'vk6.67496', 'vk6.68260', 'vk6.68415', 'vk6.69312', 'vk6.70072'] |
| 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 | O1O2O3U4O5U2U1O6O4U6U3U5 |
| R3 orbit | {'O1O2O3U4O5U2U1O6O4U6U3U5'} |
| R3 orbit length | 1 |
| Gauss code of -K | O1O2O3U4U1U5O6O5U3U2O4U6 |
| Gauss code of K* | O1O2O3U4U5U2O6U3O5O4U1U6 |
| Gauss code of -K* | O1O2O3U4U3O5O6U1O4U2U6U5 |
| 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 0 2 -1],[ 1 0 0 1 0 2 -1],[ 1 0 0 0 1 1 -1],[-1 -1 0 0 0 0 -1],[ 0 0 -1 0 0 1 -1],[-2 -2 -1 0 -1 0 0],[ 1 1 1 1 1 0 0]] |
| Primitive based matrix | [[ 0 2 1 0 -1 -1 -1],[-2 0 0 -1 0 -1 -2],[-1 0 0 0 -1 0 -1],[ 0 1 0 0 -1 -1 0],[ 1 0 1 1 0 1 1],[ 1 1 0 1 -1 0 0],[ 1 2 1 0 -1 0 0]] |
| If based matrix primitive | True |
| Phi of primitive based matrix | [-2,-1,0,1,1,1,0,1,0,1,2,0,1,0,1,1,1,0,-1,-1,0] |
| Phi over symmetry | [-2,-1,0,1,1,1,0,1,0,1,2,0,1,0,1,1,1,0,-1,-1,0] |
| Phi of -K | [-1,-1,-1,0,1,2,-1,-1,0,1,3,0,0,2,2,1,1,1,1,1,1] |
| Phi of K* | [-2,-1,0,1,1,1,1,1,1,2,3,1,1,2,1,1,0,0,0,-1,-1] |
| Phi of -K* | [-1,-1,-1,0,1,2,-1,0,0,1,2,1,1,1,0,1,0,1,0,1,0] |
| Symmetry type of based matrix | c |
| u-polynomial | -t^2+2t |
| Normalized Jones-Krushkal polynomial | 6z^2+25z+27 |
| Enhanced Jones-Krushkal polynomial | -2w^4z^2+8w^3z^2+25w^2z+27w |
| Inner characteristic polynomial | t^6+12t^4+19t^2+4 |
| Outer characteristic polynomial | t^7+20t^5+40t^3+13t |
| Flat arrow polynomial | -2*K1**2 - 4*K1*K2 + 2*K1 + K2 + 2*K3 + 2 |
| 2-strand cable arrow polynomial | 384*K1**4*K2 - 3184*K1**4 + 896*K1**3*K2*K3 + 32*K1**3*K3*K4 - 992*K1**3*K3 - 3888*K1**2*K2**2 - 1408*K1**2*K2*K4 + 6552*K1**2*K2 - 1232*K1**2*K3**2 - 176*K1**2*K4**2 - 3564*K1**2 + 64*K1*K2**3*K3 - 192*K1*K2**2*K3 - 64*K1*K2**2*K5 - 96*K1*K2*K3*K4 + 6760*K1*K2*K3 + 2176*K1*K3*K4 + 168*K1*K4*K5 - 40*K2**4 - 96*K2**2*K3**2 - 48*K2**2*K4**2 + 504*K2**2*K4 - 3108*K2**2 + 96*K2*K3*K5 + 32*K2*K4*K6 - 2200*K3**2 - 702*K4**2 - 36*K5**2 - 4*K6**2 + 3364 |
| Genus of based matrix | 1 |
| Fillings of based matrix | [[{1, 6}, {2, 5}, {3, 4}], [{2, 6}, {4, 5}, {1, 3}], [{4, 6}, {2, 5}, {1, 3}], [{5, 6}, {2, 4}, {1, 3}]] |
| If K is slice | False |