| Min(phi) over symmetries of the knot is: [-2,-1,-1,1,1,2,-1,0,1,2,2,1,0,0,1,0,1,2,0,0,1] |
| Flat knots (up to 7 crossings) with same phi are :['6.1131'] |
| 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^7+46t^5+64t^3+18t |
| Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.1131'] |
| 2-strand cable arrow polynomial of the knot is: -256*K1**4*K2**2 + 736*K1**4*K2 - 2416*K1**4 + 896*K1**3*K2*K3 - 1120*K1**3*K3 + 288*K1**2*K2**3 - 4240*K1**2*K2**2 - 672*K1**2*K2*K4 + 6736*K1**2*K2 - 1072*K1**2*K3**2 - 64*K1**2*K3*K5 - 3968*K1**2 + 64*K1*K2**3*K3 - 704*K1*K2**2*K3 - 32*K1*K2**2*K5 - 64*K1*K2*K3*K4 + 6088*K1*K2*K3 + 1592*K1*K3*K4 + 120*K1*K4*K5 - 240*K2**4 - 80*K2**2*K3**2 - 16*K2**2*K4**2 + 680*K2**2*K4 - 3172*K2**2 + 152*K2*K3*K5 + 32*K2*K4*K6 - 1900*K3**2 - 616*K4**2 - 84*K5**2 - 12*K6**2 + 3342 |
| Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.1131'] |
| Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.16928', 'vk6.17170', 'vk6.20224', 'vk6.21520', 'vk6.23322', 'vk6.23616', 'vk6.27426', 'vk6.29038', 'vk6.35357', 'vk6.35779', 'vk6.38839', 'vk6.41033', 'vk6.42838', 'vk6.43116', 'vk6.45600', 'vk6.47361', 'vk6.55088', 'vk6.55339', 'vk6.57057', 'vk6.58183', 'vk6.59487', 'vk6.59776', 'vk6.61574', 'vk6.62748', 'vk6.64931', 'vk6.65138', 'vk6.66675', 'vk6.67515', 'vk6.68224', 'vk6.68366', 'vk6.69328', 'vk6.70081'] |
| 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 | O1O2O3O4U5U2O6U4U3O5U1U6 |
| R3 orbit | {'O1O2O3O4U5U2O6U4U3O5U1U6'} |
| R3 orbit length | 1 |
| Gauss code of -K | O1O2O3O4U5U4O6U2U1O5U3U6 |
| Gauss code of K* | O1O2U3O4O5U1O6O3U6U2U5U4 |
| Gauss code of -K* | O1O2U3O4O5U1O6O3U5U4U6U2 |
| 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 1 -2 2],[ 1 0 -1 2 2 -2 2],[ 1 1 0 2 1 -1 1],[-1 -2 -2 0 0 -2 1],[-1 -2 -1 0 0 -1 0],[ 2 2 1 2 1 0 2],[-2 -2 -1 -1 0 -2 0]] |
| Primitive based matrix | [[ 0 2 1 1 -1 -1 -2],[-2 0 0 -1 -1 -2 -2],[-1 0 0 0 -1 -2 -1],[-1 1 0 0 -2 -2 -2],[ 1 1 1 2 0 1 -1],[ 1 2 2 2 -1 0 -2],[ 2 2 1 2 1 2 0]] |
| If based matrix primitive | True |
| Phi of primitive based matrix | [-2,-1,-1,1,1,2,0,1,1,2,2,0,1,2,1,2,2,2,-1,1,2] |
| Phi over symmetry | [-2,-1,-1,1,1,2,-1,0,1,2,2,1,0,0,1,0,1,2,0,0,1] |
| Phi of -K | [-2,-1,-1,1,1,2,-1,0,1,2,2,1,0,0,1,0,1,2,0,0,1] |
| Phi of K* | [-2,-1,-1,1,1,2,0,1,1,2,2,0,0,0,1,0,1,2,-1,-1,0] |
| Phi of -K* | [-2,-1,-1,1,1,2,1,2,1,2,2,1,1,2,1,2,2,2,0,0,1] |
| Symmetry type of based matrix | c |
| u-polynomial | 0 |
| 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+34t^4+38t^2+9 |
| Outer characteristic polynomial | t^7+46t^5+64t^3+18t |
| Flat arrow polynomial | -4*K1**2 - 4*K1*K2 + 2*K1 + 2*K2 + 2*K3 + 3 |
| 2-strand cable arrow polynomial | -256*K1**4*K2**2 + 736*K1**4*K2 - 2416*K1**4 + 896*K1**3*K2*K3 - 1120*K1**3*K3 + 288*K1**2*K2**3 - 4240*K1**2*K2**2 - 672*K1**2*K2*K4 + 6736*K1**2*K2 - 1072*K1**2*K3**2 - 64*K1**2*K3*K5 - 3968*K1**2 + 64*K1*K2**3*K3 - 704*K1*K2**2*K3 - 32*K1*K2**2*K5 - 64*K1*K2*K3*K4 + 6088*K1*K2*K3 + 1592*K1*K3*K4 + 120*K1*K4*K5 - 240*K2**4 - 80*K2**2*K3**2 - 16*K2**2*K4**2 + 680*K2**2*K4 - 3172*K2**2 + 152*K2*K3*K5 + 32*K2*K4*K6 - 1900*K3**2 - 616*K4**2 - 84*K5**2 - 12*K6**2 + 3342 |
| Genus of based matrix | 1 |
| Fillings of based matrix | [[{1, 6}, {3, 5}, {2, 4}], [{3, 6}, {1, 5}, {2, 4}], [{5, 6}, {1, 4}, {2, 3}], [{5, 6}, {2, 4}, {1, 3}]] |
| If K is slice | False |