| Min(phi) over symmetries of the knot is: [-3,-2,0,1,1,3,0,1,2,3,3,1,2,2,2,0,1,1,0,2,2] |
| Flat knots (up to 7 crossings) with same phi are :['6.792'] |
| Arrow polynomial of the knot is: -10*K1**2 - 4*K1*K2 + 2*K1 + 5*K2 + 2*K3 + 6 |
| Flat knots (up to 7 crossings) with same arrow polynomial are :['6.425', '6.655', '6.755', '6.769', '6.792', '6.1240', '6.1494', '6.1522', '6.1534', '6.1587', '6.1707', '6.1746', '6.1747', '6.1786', '6.1814', '6.1828', '6.1835', '6.1854', '6.1870'] |
| Outer characteristic polynomial of the knot is: t^7+60t^5+54t^3+10t |
| Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.792'] |
| 2-strand cable arrow polynomial of the knot is: -192*K1**6 - 192*K1**4*K2**2 + 1280*K1**4*K2 - 4096*K1**4 + 608*K1**3*K2*K3 + 64*K1**3*K3*K4 - 672*K1**3*K3 + 640*K1**2*K2**3 + 64*K1**2*K2**2*K4 - 4832*K1**2*K2**2 - 640*K1**2*K2*K4 + 9024*K1**2*K2 - 1344*K1**2*K3**2 - 304*K1**2*K4**2 - 5484*K1**2 + 160*K1*K2**3*K3 - 1216*K1*K2**2*K3 - 96*K1*K2**2*K5 - 320*K1*K2*K3*K4 + 7480*K1*K2*K3 - 64*K1*K2*K4*K5 + 2552*K1*K3*K4 + 440*K1*K4*K5 + 16*K1*K5*K6 - 488*K2**4 - 288*K2**2*K3**2 - 48*K2**2*K4**2 + 1232*K2**2*K4 - 4876*K2**2 - 32*K2*K3**2*K4 + 464*K2*K3*K5 + 88*K2*K4*K6 + 8*K3**2*K6 - 2800*K3**2 - 1134*K4**2 - 228*K5**2 - 20*K6**2 + 5244 |
| Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.792'] |
| Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.20005', 'vk6.20087', 'vk6.21275', 'vk6.21367', 'vk6.27052', 'vk6.27148', 'vk6.28755', 'vk6.28835', 'vk6.38445', 'vk6.38553', 'vk6.40632', 'vk6.40748', 'vk6.45325', 'vk6.45449', 'vk6.47092', 'vk6.47189', 'vk6.56820', 'vk6.56892', 'vk6.57952', 'vk6.58028', 'vk6.61334', 'vk6.61418', 'vk6.62508', 'vk6.62573', 'vk6.66532', 'vk6.66600', 'vk6.67319', 'vk6.67389', 'vk6.69174', 'vk6.69248', 'vk6.69923', 'vk6.69987'] |
| 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 | O1O2O3O4U5O6U1U6U3O5U2U4 |
| R3 orbit | {'O1O2O3O4U5O6U1U6U3O5U2U4'} |
| R3 orbit length | 1 |
| Gauss code of -K | O1O2O3O4U1U3O5U2U6U4O6U5 |
| Gauss code of K* | O1O2O3U4O5O6U1U5U3U6O4U2 |
| Gauss code of -K* | O1O2O3U2O4U5U1U6U3O5O6U4 |
| 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 3 -2 1],[ 3 0 2 2 3 1 1],[ 0 -2 0 1 2 -1 0],[-1 -2 -1 0 0 -1 0],[-3 -3 -2 0 0 -3 0],[ 2 -1 1 1 3 0 1],[-1 -1 0 0 0 -1 0]] |
| Primitive based matrix | [[ 0 3 1 1 0 -2 -3],[-3 0 0 0 -2 -3 -3],[-1 0 0 0 0 -1 -1],[-1 0 0 0 -1 -1 -2],[ 0 2 0 1 0 -1 -2],[ 2 3 1 1 1 0 -1],[ 3 3 1 2 2 1 0]] |
| If based matrix primitive | True |
| Phi of primitive based matrix | [-3,-1,-1,0,2,3,0,0,2,3,3,0,0,1,1,1,1,2,1,2,1] |
| Phi over symmetry | [-3,-2,0,1,1,3,0,1,2,3,3,1,2,2,2,0,1,1,0,2,2] |
| Phi of -K | [-3,-2,0,1,1,3,0,1,2,3,3,1,2,2,2,0,1,1,0,2,2] |
| Phi of K* | [-3,-1,-1,0,2,3,2,2,1,2,3,0,0,2,2,1,2,3,1,1,0] |
| Phi of -K* | [-3,-2,0,1,1,3,1,2,1,2,3,1,1,1,3,0,1,2,0,0,0] |
| Symmetry type of based matrix | c |
| u-polynomial | t^2-2t |
| Normalized Jones-Krushkal polynomial | z^2+22z+41 |
| Enhanced Jones-Krushkal polynomial | w^3z^2+22w^2z+41w |
| Inner characteristic polynomial | t^6+36t^4+25t^2+4 |
| Outer characteristic polynomial | t^7+60t^5+54t^3+10t |
| Flat arrow polynomial | -10*K1**2 - 4*K1*K2 + 2*K1 + 5*K2 + 2*K3 + 6 |
| 2-strand cable arrow polynomial | -192*K1**6 - 192*K1**4*K2**2 + 1280*K1**4*K2 - 4096*K1**4 + 608*K1**3*K2*K3 + 64*K1**3*K3*K4 - 672*K1**3*K3 + 640*K1**2*K2**3 + 64*K1**2*K2**2*K4 - 4832*K1**2*K2**2 - 640*K1**2*K2*K4 + 9024*K1**2*K2 - 1344*K1**2*K3**2 - 304*K1**2*K4**2 - 5484*K1**2 + 160*K1*K2**3*K3 - 1216*K1*K2**2*K3 - 96*K1*K2**2*K5 - 320*K1*K2*K3*K4 + 7480*K1*K2*K3 - 64*K1*K2*K4*K5 + 2552*K1*K3*K4 + 440*K1*K4*K5 + 16*K1*K5*K6 - 488*K2**4 - 288*K2**2*K3**2 - 48*K2**2*K4**2 + 1232*K2**2*K4 - 4876*K2**2 - 32*K2*K3**2*K4 + 464*K2*K3*K5 + 88*K2*K4*K6 + 8*K3**2*K6 - 2800*K3**2 - 1134*K4**2 - 228*K5**2 - 20*K6**2 + 5244 |
| Genus of based matrix | 1 |
| Fillings of based matrix | [[{3, 6}, {4, 5}, {1, 2}], [{4, 6}, {2, 5}, {1, 3}], [{4, 6}, {5}, {1, 3}, {2}], [{5, 6}, {3, 4}, {1, 2}]] |
| If K is slice | False |