| Min(phi) over symmetries of the knot is: [-2,-1,0,0,1,2,-1,0,1,2,2,0,1,0,1,1,0,1,0,0,1] |
| Flat knots (up to 7 crossings) with same phi are :['6.1014'] |
| Arrow polynomial of the knot is: 8*K1**3 - 12*K1**2 - 8*K1*K2 - 2*K1 + 6*K2 + 2*K3 + 7 |
| Flat knots (up to 7 crossings) with same arrow polynomial are :['6.218', '6.554', '6.929', '6.932', '6.1014', '6.1024', '6.1068', '6.1526', '6.1664', '6.1676', '6.1755', '6.1763', '6.2065', '6.2078'] |
| Outer characteristic polynomial of the knot is: t^7+41t^5+54t^3+9t |
| Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.1014'] |
| 2-strand cable arrow polynomial of the knot is: -64*K1**6 - 64*K1**4*K2**2 + 768*K1**4*K2 - 3376*K1**4 - 128*K1**3*K2**2*K3 + 480*K1**3*K2*K3 - 960*K1**3*K3 - 256*K1**2*K2**4 + 1440*K1**2*K2**3 - 7696*K1**2*K2**2 + 128*K1**2*K2*K3**2 - 640*K1**2*K2*K4 + 12040*K1**2*K2 - 528*K1**2*K3**2 - 7728*K1**2 + 1088*K1*K2**3*K3 - 1344*K1*K2**2*K3 - 192*K1*K2**2*K5 - 320*K1*K2*K3*K4 + 9224*K1*K2*K3 + 1136*K1*K3*K4 + 64*K1*K4*K5 - 192*K2**6 + 320*K2**4*K4 - 1840*K2**4 - 64*K2**3*K6 - 736*K2**2*K3**2 - 128*K2**2*K4**2 + 1840*K2**2*K4 - 5356*K2**2 + 400*K2*K3*K5 + 48*K2*K4*K6 - 2688*K3**2 - 652*K4**2 - 48*K5**2 - 4*K6**2 + 6026 |
| Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.1014'] |
| Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.16578', 'vk6.16669', 'vk6.18138', 'vk6.18474', 'vk6.22977', 'vk6.23096', 'vk6.24593', 'vk6.25006', 'vk6.34978', 'vk6.35097', 'vk6.36728', 'vk6.37147', 'vk6.42547', 'vk6.42656', 'vk6.43996', 'vk6.44308', 'vk6.54809', 'vk6.54891', 'vk6.55940', 'vk6.56236', 'vk6.59237', 'vk6.59313', 'vk6.60474', 'vk6.60836', 'vk6.64791', 'vk6.64854', 'vk6.65593', 'vk6.65900', 'vk6.68089', 'vk6.68152', 'vk6.68664', 'vk6.68875'] |
| 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 | O1O2O3O4U2U5O6U4O5U3U1U6 |
| R3 orbit | {'O1O2O3O4U2U5O6U4O5U3U1U6'} |
| R3 orbit length | 1 |
| Gauss code of -K | O1O2O3O4U5U4U2O6U1O5U6U3 |
| Gauss code of K* | O1O2O3U2U4U1U5O4O6U3O5U6 |
| Gauss code of -K* | O1O2O3U4O5U1O4O6U5U3U6U2 |
| 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 -2 0 1 0 2],[ 1 0 -2 1 2 0 2],[ 2 2 0 2 1 1 2],[ 0 -1 -2 0 1 -1 1],[-1 -2 -1 -1 0 -1 0],[ 0 0 -1 1 1 0 2],[-2 -2 -2 -1 0 -2 0]] |
| Primitive based matrix | [[ 0 2 1 0 0 -1 -2],[-2 0 0 -1 -2 -2 -2],[-1 0 0 -1 -1 -2 -1],[ 0 1 1 0 -1 -1 -2],[ 0 2 1 1 0 0 -1],[ 1 2 2 1 0 0 -2],[ 2 2 1 2 1 2 0]] |
| If based matrix primitive | True |
| Phi of primitive based matrix | [-2,-1,0,0,1,2,0,1,2,2,2,1,1,2,1,1,1,2,0,1,2] |
| Phi over symmetry | [-2,-1,0,0,1,2,-1,0,1,2,2,0,1,0,1,1,0,1,0,0,1] |
| Phi of -K | [-2,-1,0,0,1,2,-1,0,1,2,2,0,1,0,1,1,0,1,0,0,1] |
| Phi of K* | [-2,-1,0,0,1,2,1,0,1,1,2,0,0,0,2,1,1,1,0,0,-1] |
| Phi of -K* | [-2,-1,0,0,1,2,2,1,2,1,2,0,1,2,2,1,1,2,1,1,0] |
| Symmetry type of based matrix | c |
| u-polynomial | 0 |
| Normalized Jones-Krushkal polynomial | z^2+20z+37 |
| Enhanced Jones-Krushkal polynomial | w^3z^2-2w^3z+22w^2z+37w |
| Inner characteristic polynomial | t^6+31t^4+18t^2 |
| Outer characteristic polynomial | t^7+41t^5+54t^3+9t |
| Flat arrow polynomial | 8*K1**3 - 12*K1**2 - 8*K1*K2 - 2*K1 + 6*K2 + 2*K3 + 7 |
| 2-strand cable arrow polynomial | -64*K1**6 - 64*K1**4*K2**2 + 768*K1**4*K2 - 3376*K1**4 - 128*K1**3*K2**2*K3 + 480*K1**3*K2*K3 - 960*K1**3*K3 - 256*K1**2*K2**4 + 1440*K1**2*K2**3 - 7696*K1**2*K2**2 + 128*K1**2*K2*K3**2 - 640*K1**2*K2*K4 + 12040*K1**2*K2 - 528*K1**2*K3**2 - 7728*K1**2 + 1088*K1*K2**3*K3 - 1344*K1*K2**2*K3 - 192*K1*K2**2*K5 - 320*K1*K2*K3*K4 + 9224*K1*K2*K3 + 1136*K1*K3*K4 + 64*K1*K4*K5 - 192*K2**6 + 320*K2**4*K4 - 1840*K2**4 - 64*K2**3*K6 - 736*K2**2*K3**2 - 128*K2**2*K4**2 + 1840*K2**2*K4 - 5356*K2**2 + 400*K2*K3*K5 + 48*K2*K4*K6 - 2688*K3**2 - 652*K4**2 - 48*K5**2 - 4*K6**2 + 6026 |
| Genus of based matrix | 1 |
| Fillings of based matrix | [[{2, 6}, {3, 5}, {1, 4}], [{2, 6}, {5}, {1, 4}, {3}]] |
| If K is slice | False |