| Min(phi) over symmetries of the knot is: [-2,-1,0,1,1,1,0,1,1,1,2,1,1,1,1,0,1,1,0,-1,0] |
| Flat knots (up to 7 crossings) with same phi are :['6.1502', '7.39599'] |
| Arrow polynomial of the knot is: 4*K1**3 - 10*K1**2 - 4*K1*K2 - K1 + 5*K2 + K3 + 6 |
| Flat knots (up to 7 crossings) with same arrow polynomial are :['6.241', '6.341', '6.542', '6.567', '6.699', '6.713', '6.771', '6.791', '6.1025', '6.1039', '6.1041', '6.1072', '6.1077', '6.1121', '6.1123', '6.1499', '6.1502', '6.1531', '6.1645', '6.1648', '6.1726', '6.1727', '6.1761', '6.1784', '6.1807', '6.1823', '6.1832', '6.1869', '6.1873', '6.1874'] |
| Outer characteristic polynomial of the knot is: t^7+22t^5+30t^3+4t |
| Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.1502', '7.39599'] |
| 2-strand cable arrow polynomial of the knot is: -320*K1**6 - 512*K1**4*K2**2 + 3520*K1**4*K2 - 8480*K1**4 + 864*K1**3*K2*K3 - 1248*K1**3*K3 - 256*K1**2*K2**4 + 1952*K1**2*K2**3 - 10704*K1**2*K2**2 - 640*K1**2*K2*K4 + 13776*K1**2*K2 - 480*K1**2*K3**2 - 3308*K1**2 + 608*K1*K2**3*K3 - 1024*K1*K2**2*K3 - 192*K1*K2**2*K5 - 32*K1*K2*K3*K4 + 7328*K1*K2*K3 + 416*K1*K3*K4 + 24*K1*K4*K5 - 32*K2**6 + 64*K2**4*K4 - 1528*K2**4 - 32*K2**3*K6 - 240*K2**2*K3**2 - 16*K2**2*K4**2 + 1080*K2**2*K4 - 3534*K2**2 + 112*K2*K3*K5 + 16*K2*K4*K6 - 1152*K3**2 - 146*K4**2 - 12*K5**2 - 2*K6**2 + 4128 |
| Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.1502'] |
| Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.4255', 'vk6.4261', 'vk6.4334', 'vk6.4340', 'vk6.5534', 'vk6.5542', 'vk6.5653', 'vk6.5661', 'vk6.7718', 'vk6.7724', 'vk6.9120', 'vk6.9126', 'vk6.9199', 'vk6.9205', 'vk6.19832', 'vk6.19833', 'vk6.26268', 'vk6.26269', 'vk6.26712', 'vk6.26713', 'vk6.38216', 'vk6.38217', 'vk6.44993', 'vk6.44994', 'vk6.48571', 'vk6.48577', 'vk6.49284', 'vk6.49292', 'vk6.50413', 'vk6.50419', 'vk6.66356', 'vk6.66357'] |
| 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 | O1O2O3U1O4U5U3O6O5U6U4U2 |
| R3 orbit | {'O1O2O3U1O4U5U3O6O5U6U4U2'} |
| R3 orbit length | 1 |
| Gauss code of -K | O1O2O3U2U4U5O6O5U1U6O4U3 |
| Gauss code of K* | O1O2O3U4U3U5O4U2O6O5U1U6 |
| Gauss code of -K* | O1O2O3U4U3O5O4U2O6U5U1U6 |
| 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 1 1 1 0 -1],[ 2 0 2 1 1 1 0],[-1 -2 0 0 1 -1 -1],[-1 -1 0 0 0 -1 -1],[-1 -1 -1 0 0 0 -1],[ 0 -1 1 1 0 0 -1],[ 1 0 1 1 1 1 0]] |
| Primitive based matrix | [[ 0 1 1 1 0 -1 -2],[-1 0 1 0 -1 -1 -2],[-1 -1 0 0 0 -1 -1],[-1 0 0 0 -1 -1 -1],[ 0 1 0 1 0 -1 -1],[ 1 1 1 1 1 0 0],[ 2 2 1 1 1 0 0]] |
| If based matrix primitive | True |
| Phi of primitive based matrix | [-1,-1,-1,0,1,2,-1,0,1,1,2,0,0,1,1,1,1,1,1,1,0] |
| Phi over symmetry | [-2,-1,0,1,1,1,0,1,1,1,2,1,1,1,1,0,1,1,0,-1,0] |
| Phi of -K | [-2,-1,0,1,1,1,1,1,1,2,2,0,1,1,1,0,0,1,0,-1,0] |
| Phi of K* | [-1,-1,-1,0,1,2,-1,0,1,1,2,0,0,1,1,0,1,2,0,1,1] |
| Phi of -K* | [-2,-1,0,1,1,1,0,1,1,1,2,1,1,1,1,0,1,1,0,-1,0] |
| Symmetry type of based matrix | c |
| u-polynomial | t^2-2t |
| Normalized Jones-Krushkal polynomial | 2z^2+23z+39 |
| Enhanced Jones-Krushkal polynomial | 2w^3z^2+23w^2z+39w |
| Inner characteristic polynomial | t^6+14t^4+17t^2+1 |
| Outer characteristic polynomial | t^7+22t^5+30t^3+4t |
| Flat arrow polynomial | 4*K1**3 - 10*K1**2 - 4*K1*K2 - K1 + 5*K2 + K3 + 6 |
| 2-strand cable arrow polynomial | -320*K1**6 - 512*K1**4*K2**2 + 3520*K1**4*K2 - 8480*K1**4 + 864*K1**3*K2*K3 - 1248*K1**3*K3 - 256*K1**2*K2**4 + 1952*K1**2*K2**3 - 10704*K1**2*K2**2 - 640*K1**2*K2*K4 + 13776*K1**2*K2 - 480*K1**2*K3**2 - 3308*K1**2 + 608*K1*K2**3*K3 - 1024*K1*K2**2*K3 - 192*K1*K2**2*K5 - 32*K1*K2*K3*K4 + 7328*K1*K2*K3 + 416*K1*K3*K4 + 24*K1*K4*K5 - 32*K2**6 + 64*K2**4*K4 - 1528*K2**4 - 32*K2**3*K6 - 240*K2**2*K3**2 - 16*K2**2*K4**2 + 1080*K2**2*K4 - 3534*K2**2 + 112*K2*K3*K5 + 16*K2*K4*K6 - 1152*K3**2 - 146*K4**2 - 12*K5**2 - 2*K6**2 + 4128 |
| Genus of based matrix | 1 |
| Fillings of based matrix | [[{1, 6}, {2, 5}, {3, 4}], [{1, 6}, {2, 5}, {4}, {3}], [{1, 6}, {3, 5}, {2, 4}], [{1, 6}, {4, 5}, {2, 3}]] |
| If K is slice | False |